It all depends on:
(i) the quality of recording and mixing on the original song.
(ii) the quality of the recording of your added tracks and how well they're made to 'sit' within the first mix. Careful adjusting of EQs will probably be necessary as you won't be able to change the whole instruments mix that's already there.
(iii) and, most importantly, your expectations in terms of quality at the end.

It's audio so there shouldn't be any discernable degeneration as long as levels are managed, etc.
Obviously it would be better if you could do it all via WAV files rather than MP3, if that's not an issue in terms of up/downloading that might be involved, and ideally as separate tracks so that a remix can be done once the vocals are on board.
I've done 'for fun' collaborations where the backing track is an MP3 and I've added a guitar solo or vocals and the end result is fine. Not pro-studio quality of course, but fine.

John


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