Nope. Doesn't work like that, it has to be continuous play.
However, the time is divided by the number of controllers you have plugged in, so if you have 2 controllers it's only 10 hours, 3 controllers means about 7, and four controllers means you only need to wait for five hours. Note that this doesn't refer to the number of players (you can't put on 3 CPUs and say OKAY FIVE HOURS LOL), it refers to the number of controllers you have plugged in. If you're one guy with 3 controllers, then woot woot, time cut!
Make sure your system is well-ventilated if you're gonna do this. Just play an endless melee (timed match set to infinity) and let the computers kick you around for X hours. Then do the no contest and you'll face Mewtwo.
I'm at 98% SSE completion. There are a couple things we just can't find no matter how hard we look.