So, what would happen if I pulled the 2164 out of an FB-01 and stuck in a 2612 instead? Would I just end up with a fried 2612? If so, would it be possible to modify an FB-01 to work with a 2612?
Sadly it wouldn't work, there are some differences:
2612 has analog output, 2151 has digital output (needs external DAC)
2612 has different registers and register functions compared to 2151
FB-01 software won't know how to program the 2612
The YM2612 manual seems to suggest it's possible to take YM2151-designed music and play it on the YM2612 as long as you observe some limitations. For SMS emulation I had used a OPL-2 sound chip (YM3812) to play back the YM2413 sound which wasn't perfect but sounded better than you'd think, though the source material was not written with any 3812 limitations in mind.
So maybe it would be possible to write YM2612 tunes this way, though it largely depends on the FB-01 implements software-based features like (I guess) vibrato, frequency/volume slides, etc. Probably too much trouble.