Off hand I would say no. I believe, baseboard heat uses water at a
higher temperature (190 degrees) than radiant (around 120 I think). I
have the same setup and I cut the cabinet to go around the baseboard
heat and the bathroom is still warm. If it is a eyesore, replace the
baseboard housing with a new one.

If you still want radiant heat, they make heating elements that go
under the tile that will warm the room and possibly heat the room.
This would be a lot easier to install than running pipes in the floor.