Assuming custom moves will be legal, the main problem would be accessibility. This problem won't matter on the 3DS version because everyone will have their own console, as said above. But for the Wii U version, it can be.
I assume custom moves will be saved to the person's name they create, like custom controls in Brawl. Customizing moves looks pretty easy, if this is how it works. Create your name (like everyone does in tourneys nowadays) and set up your controls and custom moves.
As for stats, I am under the assumption that they must first be enabled and customized before they even have an effect on your character. The only way they'd affect the game would be if someone added stats prior to turning on the Wii U, in which case, TOs should always check to see if someone is potentially cheating this way.
I, personally, am for custom moves and against stats. However, this will need to be discussed in a large scale by more professional players and TOs when the game is launched, or near launch for the Wii U version.
Whether or not custom moves are allowed, I'm gonna jump a bit to a certain character. Palutena's whole gimmick is custom moves, so people that use her should be given an exception.