Not that I wouldn't have slyly let it slide, back in the day, but it is wrong on the deepest, truest level, and stupid up here on the shallow and profane one, because they WILL snag you two or three months down the line, and you will have falsely and foolishly invested a ton of emotional energy into thinking you beat the system in the meanitime, when you could immediately free yourself with the truth right now.
Doing the right thing, I have finally come to believe, is not only the right thing, but the smart thing too.
Go for it.