Yes, It's been tried. One I know of in the SEDiv SCCA is Kevin Beaver. I don't want to put words in his mouth but he and OPM put a lot of time and effort into a no-excuses NA1.6. And he did very well, usually running near the front, about 1 sec/lap slower than the fastest lapper in the field. Then (again, my words not his) he got tired of beating his head against the wall and built an NB.
I think on a regional level you might do OK. On a Majors/HST level probably not a snowball's chance.
How did he do in the NB? He seemed about a second off there as well?