Probably. But the President can't tell the FCC commissioners what to say. He can replace them with people who are more sympathetic towards his administration's position. But he can't order them to parrot his position or rubber stamp it.
This opens things up considerably now that the FCC is down on record as saying there's a "reasonable expectation of privacy" for mobile communications. It gives the courts room to step in and rule on the broader constitutional issue if/when this becomes a disputed decree.
Replacing the currently sitting commission membership with an entirely new slate won't make that legal question go away.
It was a brilliant maneuver on the part of the FCC.