As a paint and body man with 25+ years of experience, I can tell you this. Rust is like a cancer, the only way to properly repair it is to cut it out or to kill it in its tracks. As johnny said, do it right the first time. After you see how bad the damamge is , you must make the decision on which way is the permanent cure.
Yes you can weld in patches. But only if you have taken the steps to kill the rust. That means either blasting the affected ares or treating them chemically to remove it. Then cut out the ragged stuff to make easy to deal with edges and weld her up. After you must seal all the seams and treat the area with a corrosion resistant primer to prevent further infection. And rattle can primer or laquer based hot rod stuff wont work.
If you need any advice feel free to ask.
Posting pics after you get the carpet out and get it cleaned up would be great. I will be glad to help you on you decision.