Communication is a well-understood problem, and SpaceX already has Starlink. They might need pretty high bandwidth, but that's not necessarily much of a problem in space. Latency could be a problem, except that AI training isn't the sort of problem where you care about latency.

I'd be curious where exactly they plan to put these datacenters... In low Earth orbit they would eventually reenter, which makes them a pollution source and you'd have no solar power half the time.

Parking them at the Earth-Sun L1 point would be better for solar power, but it would be more expensive to get stuff there.