I'm even less knowledgeable about the 4T45 than I am about the 2.2L, but a quicks search tells me that trans would be iffy around 400, and is better suited to the low 300whp range. Granted, that information came from a Grand Am forum, and it's likely to live longer in an easier life in the back of a Goblin. I know the RWD 4L60's lifespan was inversely proportionate to how much heat they saw, and I'd imagine the same would apply to a 4T45 with some power put to it.
I found a company selling tunes for the HHR SS which has the same 2.0T as the Cobalt SS/TC. Their Stage 1 tune on a manual trans takes the motor from 260/260 at the crank to 290/340 at the tire, whereas an auto goes from 220 hp at the crank to 280/300 at the tire, so take that for what it's worth.
The 2.2 probably needs rods and pistons to live at 400, and definitely needs a fuel pump and injectors to get there.
Keep in mind, too, if the Goblin you're looking at is built off of a 2005 or 2006 2.2L, then its computer can't be tuned, and you're looking at a lot more work to make any more than factory power.