Are you allowed to change your seats in the stock category according to SCCA rules?

Short answer....no.

Long answer....sort of....let me explain:

If a car produced within your series offered an upgraded seat, such as the Recaro's that come with the G85 package, you are allowed to update to that seat provided you install EVERYTHING associated with the package. In the case of the Cobalt SS/SC, if you ordered it without the G85 package, you would have to not only include the seats, but also interior trim, limited slip differential, any included suspension changes, any differences in trim, all comfort and convenience items, etc. Essentially you would wind up having to build your own G85 without leaving a darn thing out.

If you check the SCCA website, under the rules section you can download several PDF's.
There are several that cover your class and what is allowed as you move through the classes. For example, new seats but street tires might take you to Street Touring STS.
If you add the Quaife LSD, and the seats, that may take you to STX. If you use slicks with that set up, that might take you to street modified.
It is conceivable that these mods might reduce your raw time, but as you change classes your PAX time will reflect your class.

All of this is fine of course, but remember the competition. There is always someone with more $$$ and more wheel time. A better idea, before you mod up, is to work on your driving. Find one of the gray beards at your region to ride with you and straighten out your game. Even if you think you are driving at the top of your game, experience wins out and those old guys know their stuff, they usually have tips that will shave more time in your current class than if you were to follow the GM build book and take your ECOTEC to 1300HP.

Additionally, I'm not sure everyone will allow you to "track date" an "LS" to an "SS Supercharged" without doing the full deed, engine, trans, etc. It will depend on the people in your region and how intense they are about things. For the most part, the people I have met in the SCCA are some of the coolest folks out there. However, be prepared to run into some serious knowledge and folks who will want to re-class you due to an aftermarket shift knob. Once you hit the national level, there are people who will learn the part numbers for your car and scrutinize parts you never thought about replacing. I once saw a guy who brought a laptop (to a local event) that had an enormous database of cars and trim levels and parts etc. Just to try and discredit his competitors. I guess I can see both sides, my stuff has always been stock, but you never know if someone is trying to get one over on you. I guess I'm glad dude is there to keep things fair, and he can be the guy poking through everyone's stuff.

Unless you plan to go all in, I suggest you stick to having fun, and focusing on driving your best, shaving a second or two here and there.
If you plan to go all in, though, best of luck and let me know how it works out!