Go for it! Removing having to think about the transmission and coordinate your hand with your foot with your other foot with the other half of your other foot while yet another damned 3-series just can't wait to get around you when you're trying to remember what rpm you need to be at for 23.7mph in 2nd gear is a big help for getting started and getting comfortable driving on track. I am admittedly very lazy, and almost all of my races have been in automatics, and, even with the shiftable ones, its nice to not have to worry about the coordination and the timing and getting the rev match just right so you don't have to upset the chassis, etc.
The internet tells me that people rarely have problems with that transmission, even in boosted applications, and that it's an Aisin unit that's spec'd for a whole lot more power than the little 2.0 can put out, and is shared with some RWD Lexus vehicles with the smaller V6. I can't imagine it being problematic - as others have said, get the largest (height, width, and especially depth) cooler that you can find, get some sort of large gauge for it (the Buick pulls this info from the computer, and starts flashing bright red if it gets over a certain temperature), and you're good to go. Even if it does get too hot, you have the benefit of shiftability, so, theoretically, you can just lock it in 4th and turn some laps until it cools back down - but, if you put a good, oversized cooler on it, I highly doubt you'd have temperature issues.
Semi-Sentient Centenarians
1996 Buick Century - we upgraded our crappy GM sedan with parts from a crappy GM minivan.
"It's got a van motor, a 220 cubic inch plant, it's got van tires, van suspension, van shocks. It's a model with the catalytic converters ripped out so
it'll run good on regular gas. What do you say, is it a racecar or what?" - Blues Brothers, Probably