Not the same as your idea, but similar is NINJAM, which is tempo synced, but deliberately makes the latency equal to one bar, phrase, or other segment of time. You are always playing live to what everyone else played the very last time around, but you are still playing on the beat together. It obviously works better for repetitive jam sessions than for structured songs, but it looks very interesting. I haven't yet tried it with my music buddies, and should.

[1] https://www.cockos.com/ninjam/