Yes but would these need to be in LEO? I would imagine that they would aim for farther orbits to spend a smaller percentage of their time in Earth's shadow
I still cannot believe it's economical to have "data centers in orbit" but I guess the truth will be seen in whether or not it actually happens.
The FCC has regulatory jurisdiction for communications on US objects in space, regardless of distance from earth.
Even very optimistic estimates (by people who aren't Elon Musk) say it will take a decade to get the costs low enough to be worthwhile for LEO; higher orbits are much more expensive.