ME3 Multiplayer on XBox One with Backwards Compatibility

Save files do transfer (if you use cloud storage on 360) and AFAIK your MP progress is synced with your EA account anyway.

However, Mass Effect 3 is not in the first wave of 104 games and ii is not mentioned among the few games previewd to be added in December update. Right now the only backward compatible BioWare game is Mass Effect 1, which was published by Microsoft.