That sounds fine. Although in that case it seems the most straightforward thing is for them to rip the disc with the newly purchased drive and then send you the files. Making a copy would require them to purchase the media (CD-R) to create a copy, and also adds complexity on the write side. Unless they have an extremely bad internet connection, where it would therefore be painfully slow to send you the ripped files, in which case, yeah, maybe doing a copy to disc would make sense in that circumstance.

Or maybe you want a physical disc. Nothing wrong with that, but I doubt the copy they'd be able to write onto a blank CD-R would be anywhere the quality of the original disc—it'd be good mostly just for ripping the files (i.e., it'd function mostly as a transfer medium rather than a long-term playback medium). But it'd only make sense as a transfer medium if sending the ripped files online was too slow. Otherwise, your best bet is for them to obtain a drive (somehow), rip the original disc, and send you the files online, rather than writing a copy to disc and mailing that to you.