Hmmm.. to be honest, probably not. The only way to have a chance is to get R-compound tires, which oddly enough are legal in stock class. You'll be up against 2.3l Focus', Mini Coopers (non S), and the like. The suspension setups are far superior to anything our old Triumphs have....
With the being said, one of the quickest cars at our local auto-x events was a nearly stock 83 VW rabbit. It had no interior, and racing tires, but an essentially stock motor; and he embarrassed almost everyone on the track. What I'm trying to say that car vs. car you'll probably lose, but if you're a good driver then I'd say you'd have a better than average chance. If you don't have that much experience, then practice, practice, practice!
I'd still get some R-compound tires, it makes it that much more fun.