There is no legal obligation to be truthful in what one places on their Facebook profile, however, so it's not perjuring. You can out on whatever you like and it's up to the border agent to make of it whatever they will.
In criminal law, intention matters as much as actions.
I suspect the that deliberately creating a false profile would push you into perjury territory. And in any case, even if the rulings come down otherwise, you'll still get arrested and remanded for a long time while the lawyers sort it out.
Again, though: I am not a lawyer. Consult a lawyer.
