Oh, it'd definitely be legal if there weren't the prizes (or if the prizes were, say, 5% health, not invincibility star). It could well be a neutral stage (see: Castle Siege) though it seems more abusable than Castle Siege as DeDeDe due to the greater frequency of the walk-off edges.
To me, the problem lies in the "Dodge!" section, where the racing car randomly stops or does an instant race thru the stage. Noone can predict what it will do, so that mini-game would probably ruin Wario Wares chances of being legal.
Uh, no? Its not at all hard to dodge. Seriously, even though it is random, it isn't that difficult to dodge it either way.
If you spent a half hour learning how to play the level, you'd know how to win and take advantage of every minigame, easy.
And dodging the foot is a joke. If you can't dodge it, your opponent put you in it.
Likewise with the rain; it creates an interesting fight under the umbrella.
If there weren't prizes for winning the minigames, it'd could well be a neutral stage. Yeah, the minigames are generally good for DeDeDe, but the main part of the stage is like two CGs long. Castle Seige is a neutral with walk-offs, after all, and I doubt Warioware has them for any higher percentage of the time (though to be entirely fair it is rather different, as the walk-offs appear more often, even if they don't last nearly as long).
Not sure if it'd be neutral, but it seems like it'd be close.