The Wii U hardware can handle two gamepads at once, but most software doesn't allow it. If smash 4 allows two gamepads to be used at once, the tournament rules will almost assuredly be that they're legal, but if more than two players want to use them in doubles, each team is allotted one. If smash 4 only allows one gamepad at a time, they'll be tournament banned.
As per whether you should use it, your own personal screen could offer some small advantages (face away from your opponent, hide button inputs), but it's a bit large for a competitive controller and worse yet pretty expensive. Let's be real; your tournament controllers get treated harshly. You not only play hard on them (pressing a lot of things fast and rough, using them a crazy amount), but you carry them around everywhere which is a serious source of wear and tear itself and would make it hard to avoid scratching up your gamepad's screen. The advantages offered would have to be pretty massive for me to consider using the gamepad for smash, and I have a feeling most players will feel the same way.
EDIT: As per lag, there are plenty of options to get lagless displays. I suggest against getting a TV at all; get an HD monitor as those tend to be much better. I suggest checking this database:
http://www.displaylag.com/display-database/
I have a 27" LG that is the third monitor on the list, and it's pretty amazing (9 ms of lag is not something you're going to notice, and it's faster than the one frame you claim the gamepad has) with the secondary benefit that it only costs a few hundred dollars.
