Those compressors pump out ALLOT of heat dude. Liek ALLOT of heat. Whatever room your going to put it in is going to get pretty damn hot, pretty damn quick. Not to mention, very moist. And while they are not SUPER loud, they are not super quiet either.
I mean, its worth a try. Don't know how big your basement really is. But FYI, it is going to run more than an hour if it is a nice energy effecient unit. They have an inverter that can modulate the amperage to the compressor. So effectively, the system only needs to work as hard as it needs to. It's not an on and off deal like a typical home air con. So what happens is that the air conditioner kind of settles on a set cooling rate needed based on your heat load and then it quietly humms away.
I fucking love my mini split. It really is some super pimp shit.