If I'm understanding your question correctly, you're asking if I've run into situations where console hiccups interfere with the music, correct?
Well yes, and no. It really depends on the hardware. When I'm making Gameboy music, I'd have to overclock the CPU or set the BPM to even remotely have it affect playback in any meaningful way. There is, however, the quirk of the Gameboy background hum, which comes from the speakers and can muddy mixes. For my final mixes, I get around this by recording the song from an emulator.
For Super Nintendo music, it's a little different. The CPU is a lot more powerful, so the system pretty much never crashes. However, because samples hog memory like crazy, I can sometimes run out of song space if I'm not careful. I get around this by stitching multiple song files together in a game. More annoyingly, if I'm controlling the Super Nintendo with a keyboard, sometimes the notes don't register that I've let go and ring out for eternity.