I did some experimentation with this recently; added a 2K option ROM (the smallest BIOSes will actually handle sanely) that just mapped requests for tracks on Drive A to bits of the ROM address space. The problem is getting enough disc image space-- your limiter there is almost certainly the sockets an 5150 board offers. I use a machine with a custom memory card that uses a 39SF010 (128k flash) for E000 and F000, so I had 90k left once the "real" BIOS stuff was added. This holds a DOS 2.11 image with DEBUG, EDLIN, FORMAT, and SYS, so you could theoretically black-start a machine with no formatted media. Alternative payloads would be boot-to-game, boot-to-specific-application, etc.
I could see using a larger ROM still, say a 39SF020 (256k) but enabled at C800-F7FF to give 192k of usable ROM, that's definitely enough to hold an unretouched 180k single-sided disc image.