I have been in the planning stages for my blazer ever since I have gotten it (about a 1 1/2 years) and I have finally settled after reading all the info on the performance parts to get a supercharger at 7psi, JBA headers, and exhaust to about 2 3/4 in (figure I can go a little wider than the 2 1/2 with the supercharger), and I also plan on putting in a cold air intake. Then of course I need to get it tuned for all the changes (one change at a time though due to funding, supercharger last). So I figure I might be pushing around 300 hp to the crank give or take some.

So I was curious if the engine and tranny could hold up to this increase in power while keeping engine stock (other than above upgrades) and not modifying the transmission at all?

 

hp, tranny don't really care about hp.

What kind of torque are you pushing?
Tranny care about torque.

 

Through my calculations I will probably have about 370 ft lbs of tq

 

You should fine if you don't abuse it.
A stock 4.3L V6 engine pushes 250ft pounds.
It can be rebuilt to handle 450ft pounds.