Indeed, the structure of the Commission is designed for that. Although Commissioners are appointed by the President and approved by the Senate, by law no more than 3 of the 5 can be from the same party. Traditionally for the two Commissioners not of his party the President nominates whoever the Senate leader of the other party recommends, and traditionally if that party is the minority party in the Senate the senators from the majority party pretty much rubber stamp it, so in practice the party that controls the White House gets a pretty free choice for three of the seats, and the other party gets a pretty free choice for the other two seats.
He doesn't "work for" the FCC, he's a commissioner [1], which is a political position for which he was nominated. The role is inherently political and he's there to provide leadership. He's a Democrat, if anything this means he's more likely to find a higher role in the future.