It is quite important to test for bit-perfect-ness because sometimes you get surprises.
For example, that old junk CD723 had an undithered digital volume control that couldn't be set to 0dB. Its maximum setting was a bit lower than 0dB. So it would multiply all the digital data by something like 0.99 and then truncate it to 16 bits, who cares about dither. It did that even on the SPDIF output, so I recorded it on the PC, ABX'd it versus the ripped CD, and the buggy processing in the CDP was definitely audible. It manifested as all the sweet reverb and details disappearing. It makes perfect sense, because a proper CD with at least 12-16dB dynamic range uses only 11-12 bits most of the time, so you really need that LSB dithering that's embedded in the recording, and messing with the LSB destroys the mastering engineer's good dithering job.
How to test a CD player for bit-perfectness:
Burn a CD with a test WAV, play it on the CDP, record the SPDIF output with your soundcard, and compare the files. I used to do that with a python script so can't recommend software, but on linux you can also just use diff. You should use a software that will skip the extra silence at the beginning of your recording. If the two files are identical (except the silence of course) then it is bit-perfect.
You can do the same test by recording the output of the CDP, then ripping the CD, and comparing the files. They should be identical, minus the silence at the beginning and end.
You can do the same with your soundcard in loopback. Output a WAV on the SPDIF output, record it, compare. It is quite useful to detect driver or software bugs that will do funny things to the audio, or that sneaky windows resampler.
You will most likely be disappointed though: all properly working CDPs will read a CD bit-perfect, unless there is a firmware bug like CD723. I tested a €30 multi-MP3-DVD player and of course the digital output was perfect. Absolutely all the audiophile woo about transports is just superstition. Green markers, blah blah, gold plated CD-Rs, this has zero effects on the actual data.
Likewise all soundcards are bit-perfect if used in a mode that enables it, like ASIO, unless there are bugs or special sound effect options that can be enabled or disabled separately.
Digital audio read from a CD is bit-for-bit identical to the same file played on a computer's SPDIF output (unless, as said above, the drivers do funny stuff, but it you test it, you can check that the bits are the same). Likewise the bits are the same on optical or coax, no matter how much the cable costs.
SPDIF includes error checking codes. If you want to experiment you can wire a LED to the ERROR output of the SPDIF decoder. The only way to light it is to unplug the SPDIF optical fiber. It is very robust.
So, do the test, and most likely if your hardware is working and your software is not buggy, you will find out that all the bits are transmitted perfectly. This is important, because instead of wasting time on woo-woo, you can fix actual problems and make actual improvements.
If there are differences in sound quality between two transports, using the same DAC, and both are functional (ie, bit-perfect) then the differences are entirely due to clock jitter and EMI. This is another huge can of worms, which tends to be called "woo-woo" by objectivists.
Yes you can measure a difference in jitter by placing a brick (or the gold plated audiophile equivalent, probably granite) on the transport, or mess with these cute spiky feets, etc. It tends to not be relevant, and to indicate the device is cheaply designed, but the effect exists.
So yes there are huge sound quality differences between transports, and it's not the bits, it's jitter and EMI, and what it mostly indicates is the DAC's inability to do its job of rejecting that. So if a transport sounds a lot better than another, it's not because the transport is great, it's because the DAC sucks. It's like the suspension on a car. If "this road feels so much better than this other one", it's not really the road, just fix the suspension.
Important: If your transport does "upsampling" (the marketing term for "oversampling") then the bits on the SPDIF output are not the bits on the CD, because the signal was oversampled. If the algorithm is not buggy, this is absolutely fine, but if you want to test for bit-perfect-ness, of course you should disable it for the test. Likewise if you do the test with the soundcard, make sure there isn't a sample rate conversion plugin somewhere in the chain. Otherwise you get an original 44.1k WAV and a (say) 192k recorded wav, and there is no point in comparing them.
The question mark is how perfect the read from a CD will be to the sound card.
It will be what's on the disk, unless the CDP is buggy or upsamples.
There is a difference with scratched CDs though: if there is a read error, which is very rare but happens if it is badly scratched, the CDP will hide it by interpolating the missing sample from its neighbors. So you may get an occasional sample that differs from the actual data on disk, if the CD is damaged. That's actually what you want, it's better than a loud click due to a read error. If the CD is in reasonably good condition, it NEVER happens.
If your goal is to rip CDs, just do it with your computer. Use Exact Audio Copy and make sure the drive in the PC reports C2 errors correctly, so if a CD is scratched, it will read again or give up, and not output a WAV file with loud clicks. This gives bit-perfect rips.
Now if your goal is to listen to the CD, then... just sell the CD player, and play the ripped file on your computer with the soundcard slaved to the DAC's wordclock output. If the DAC has a master clock, this option ensures the least possible amount of jitter.
Also there is confusion: word clock has nothing to do with bits, in fact it has nothing to do with the data. It's about synchronization. If you use several ADCs in your recording studio you want them all synchronized so the tracks line up sample by sample, so they have to be synced by word clock. And in your case, the DAC outputs a clock and the soundcard synchronizes itself to it, so the DAC doesn't have to do the jitter rejection job.
Storytime
How to make a CD player sound better with a brick.
Due to vibrations in the room, like music being played, everything vibrates, including the spinning CD. It also wobbles because it can never be perfectly flat and centered. Likewise the track itself is not a perfect spiral, it can have some wobble.
The actuator coils in the optical pick-up keep the lens assembly aligned with the track, both horizontally and vertically. It's a pretty tough job, because the track is only 500nm wide and going very fast past the lens. So the coils eat up quite a lot of current to do the job.
And... the actuator coil current pretty much mirrors any vibration on the CD. This draws current from the power supply depending on ambient noise, vibration, ripple in the track, etc. It's basically a large microphone.
If the power supply is cheap enough, and you stick a scope probe in it, you will notice a huge amount of ripple that depends on ambient noise. On the CD723 it was so bad that someone walking in the room would cause the power supply to dance on the scope, just from vibration. Due to the low PSRR of the logic supply, this found its way into the rest of the circuit, and as a result SPDIF output jitter was visible to the naked eye on the scope, with the SPDIF trace wiggling around at the slightest vibration.
The usual audiophile solution is to make a very expensive and heavy machined aluminium chassis (or put a brick on it). A better solution is to build a proper power supply with the important bits having good PSRR. Or just use a computer to play the digital file, which removes the problem.
And so all the audiophile tweaks, the spiky feet, the granite slabs, the super heavy stands, all the woo-woo, it actually does something. It works! It solves the completely wrong problem, which is actually PSRR, but it's not magic at all. And the more it works, the more you know the CDP's power supply's low PSRR feeds the ripple from actuator coil current where it shouldn't be, and is therefore garbage.