My jeep is "light kaki".
I read in a street racing magazine that did an article on a 1000+hp integra was running with the stock transmission.
OK, here is where I do see a major problem. You should definitely be worried. People built up the GM 3800's enough to where the starter ring gear bolts were backing out. Input shafts snapped. CV joints were exploding.
FWIW - a supercharger is going to add more torque off the line and will be harder on the transmission. A turbo kicks in as RPM's build and are easier on hardened components in the transmission. The trans needs to be capable and designed to hold up to the demands you're going to put on it. I'm not saying the KJ trans can't handle it - I don't really know. I am just saying that you can't say because an Integra did it that anything can. Sometimes (the majority of the time) it's just not going to be possible or feasible.
You'll need to look at fueling - is the stock fuel pump enough? Injectors? You will definitely need a tune, and you'll also need the ability to scan/log constantly for knock and such (tool such as Autotap is critical). You're going into unchartered territory, therefore there's no cookie cutter approach. It'll be very easy to detonate.
I'm not trying to sway you, just really think it all out before you start going down that road. Think about how many miles you'll have on the KJ before you're ready. I was going to drive my Grand Prix forever, I was going to turbo it (yes, there's a pre-fabbed kit to bolt on a turbo and run 11's). Well, plans change - look where I am, on jeepkj.com. Hell, 6 months ago I was still planning on getting it cleaned up and working on it some more this summer. PLans can change, IMO have your daily driver that you mod slightly to your liking that can still be reliable, and then have your fun car. I have my KJ now that'll receive minor mods, and my '68 Austin Healey that will soon be torn down to rebuild into a custom classic. All I am saying is you'll love it dearly and think you're going to keep it forever, then life plans change. The Prix isn't useful to me anymore. It's a two door, my friends don't want to climb in the back. It's a car - I am a homeowner now and I need to have some cargo room for various things. Life changes, really plan the whole project out before you dig yourself into a hole.