Well, for starters, that kit doesn't include anything for the fuel modifications you'll need to make, so there's more money into it. Plus modifying the exhaust (the I5 has one of it's cats as an integral part of the exhaust manifold I believe). Figuring out how to plumb the intercooler will probably be a pain, especially since the piping they provide doesn't look at all to be custom but just some generic bends that you'll end up having to cut and probably buy more of.
Plus I really think the I5 is already pushing itself close to it's limits already and trying to boost it will be potentially very costly if you end up blowing the motor, which happens fairly frequently when boosting. I know some of the Colorado guys have done it, but I don't think it's worth it for our vehicles. Turbos make most of their power in the upper bands, outside of the rpm range you'll usually use in a Hummer. Unless you like breaking everything. A supercharger would be a better idea, but still you're stuck with the issue of not blowing up your engine accidentally.
I think it was Nugget on here from Australia who tried both a turbo and a supercharger (I think he tried both) and both times he ended up blowing the motor at least once. And that was with a shop helping him I think. He gave up and left it stock afterwards. They don't really overdesign the smaller engines anymore these days, thanks to their fancy computer systems that let them build it strong enough to not fall apart, but so that they also save on material and manufacturing costs. I think that's why you're not even supposed to bore the cylinder sleeves for the I5, if they are worn, you're supposed to flat out replace them. They are probably just thick enough that it's probably not safe to try and bore them. The V8's are probably a different matter, since a lot of times those end up in the muscle cars and of course people are going to push those things. Even then you're usually better off going up a size or two in displacement.
So you're welcome to try, but I would suggest rethinking the idea. You'd probably end up looking at spending at least a few thousand, if not more. And with that much you might as well just get an Alpha and not worry about reliability so much.