The 100/500mA maximum that the MCP73831 will provide can be used by the battery, or the load, or both sharing it, which means @ the 500mA setting & if your load is operating at its maximum ~300mA, there'll only be ~200mA available to charge your battery, so it'll take longer to charge.
This arrangement is only appropriate to power electronics that can operate between 4.2V (LiPo fully charged) to around 3.0V (LiPo dead flat), and within the 100/500mA charge current capability. So the load will get whatever voltage is determined by the LiPo's state of charge. The load could potentially draw more than 500mA, in which case up to 500mA is coming from the 73831, and the rest from the LiPo. This isn't necessarily a bad thing, it all depends on what the 'load' is, and it can be a valid design decision.
If you're powering, for example, an AVR8 MCU (e.g. ATmega328p, to choose the most common example, but many others are similar), this is fine, although the 'Safe Operating Area' (search for 'Speed Grades' in the '328 datasheet) for that chip won't let you reliably operate down to that low of a Vcc at the usual 16MHz, you'll need to set the pre-scaler to operate the CPU (F_CPU) at 8 or 10 MHz (with the normal 16MHz crystal).
Lastly, if you're being powered from USB, keep in mind that some computer USB ports are truly designed to USB spec, and will only let you draw 100mA without enumerating onto the USB bus (which neither that chip nor the SparkFun PCB do, you need an entire USB-capable MCU to do that), although most smartphone/etc chargers will happily let you draw 500mA or more without enumeration.