The stock rear and tranny might hold up for a while then, but it's still a roll of the dice, so just be mindful of it.
Ethan brings up a valid concern for you. If I may suggest putting on a BIG transmission cooler (after it runs through the radiator) and a big inline/external filter. That'll keep the transmission temps down and let you change the external trans filter on a regular basis (did mine with every engine oil change) while adding a new fresh quart of fluid. That should prolong the life of the 200R4 and keep shifts as crisp as they can be - it'll also be a good gauge on how well the transmission is doing if you cut the filter open and see what is being caught by the filter.
Another point well made is the rear-end. I blew up a couple rear ends before putting in the 9" (which I consider one of the best investments I made - along with the TH400). I built an IROC with about 415 crank HP (331 rwhp on a DynoJet) for my wife back in 2002 and didn't want to buy a 9" for it unless I had too. I installed one of the cast aluminum rear covers and it held up for a number of drag strip outings on slicks and included a few passes on a 150 shot right out of the gate. So, I think the cast covers are well worth the money to help prevent or at least prolong the small pinion gear in these SS's with the 3.73 gears from exploding.
There are a number of people that sell them. The one I like is the LPW Ultimate (LPW 301-7.5G) - it has a provision for added additional bracing (LPW 341-A) for the axle housings. You have to weld on a couple tabs to the axle and the "kit" is an additional $125 or so - if you wouldn't add the additional bracing any of the other similar cast differential braces out there would do.
Here's a picture of the LPW cover with the bracing.