TLDR yes, just grab an IDE drive. You might find some SATA DVD drives that still has the analog audio connector, but don't be fooled by that. More often than not those connectors are duds. I'd say the definitive give away that a drive supports analog CD audio is the presence of a play/stop button on its chassis. Without that, I'd be pessimistic.
It is just easier to grab an IDE CD drive and connect it.
Also, if you are using WinXP, you can get CD audio without the need for the analog CD audio cable altogether. But older OSes don't have this facility to my knowledge.
Turbo XT 12MHz, EGA, MFM HDD
Intel 386 DX-33, Speedstar 24X, SB 1.5, 1x CD
Intel 486 DX2-66, CL5428 VLB, SBPro 2, 2x CD
IBM BlueLightning 100MHz, CL5428, SB16, 4x CD
Intel Pentium 90, Matrox Millenium 2, SB16, 4x CD
HP Z400, Xeon 3.46GHz, YMF-744, RTX2060