dessert's test exactly answers David's question.
But as said im my comment, we have three possible states for DVD-R.
To distinguish them all, one may use cdrskin option -minfo.
(Note well: -minfo without the "s" of -msinfo.)
cdrskin dev=/dev/sr0 -minfo 2>/dev/null | grep '^disk status:'
This should yield 4 possible text results on standard output.
With a blank medium (unused and writable):
disk status: empty
With an appendable medium (written and still writable):
disk status: incomplete/appendable
With a closed medium (written and not writable any more):
disk status: complete
As fourth possible result, if something goes wrong with accessing the
medium, no text at all will appear. In this case you should repeat the
run without 2>/dev/null | grep '^disk status:' in order
to see all messages.
(I use /dev/sr0 in the example, because /dev/hdc
is out of fashion as device name since at least kernel version 3.)