He has. Rampage aka Stuart Clark aka the "new" Jigsaw www.comicvine.com/rampage/29-15416/
In a storyline that I hated, Frank killed Stuart's girlfriend under that influence of the Hate-Monger. He never told Stuart, who considered Frank his friend. When Stuart found out he snapped and joined up with Jigsaw. Granted he started out as a villain but he didn't deserve that and an innocent died by Frank's hands. I dropped 616 Punisher after that story and jumped in sporadic to keep up.
Rampage was already a villain, although he had somewhat reformed.
You could argue for Jigsaw. He was a bog standard mobster prior to Frank cutting him up and turning him into a true psychotic and his long standing nemesis.
I cant recall an example of Franks actions turning a true innocent into a costumed villain though.