No, probably not there are no phase issues if you just don't transmit the signal. The hard part would be to determine who's in the room, and then who's talking and then mixing appropriately to eliminate feedback and optimize speaker sound quality. None of which requires signal phase accurate synchronicity.
If they're actually able to "sync" (again a poorly defined term) given the problems associated with network latency and different hardware it would border on magic.
If they're actually able to "sync" (again a poorly defined term) given the problems associated with network latency and different hardware it would border on magic.