Kind of, yeah. But real Open Level professional tennis didn't really exist until two things happened:
1) Pro Tennis opened the tournaments (especially the grand slams) to all comers, and...
2) A generation of young athletes had the chance to know this, watch the tennis boom hit, practice, come of age, and compete in a suddenly viable professional sport that rewarded competition more than just glorified exhibition play.
The old guys winning "Slams" before the mid 70's were just the well-practiced ex-pros who had no young talent to compete against before, since there wasn't a real professional living to be made or prestige to be gained, previously. Yeah, the top couple guys could earn, but that's no way to stock a supposed "Open athletic event" with honest athletic talent. The "pro tour" of the 50's and 60's was comprised of a few dozen mediocre athletes playing each other for spectacle. It had more in common with modern day pro wrestling than modern day tennis. By the time the first legitimate, modern, pro-level players were on the scene (Connors, Borg, Vilas), that kind of grandfathering in was no longer possible.
All of which is to say that Rosewall, Laver, etc. weren't nearly the players they're made out to be by historians desperate to cling to nostalgia. They were compilers competing against mostly fellow Australian 5'6" midgets.
Agassi is the *most accurate* answer to this question, as the oldest slam winner of the legitimately athletic pro era. But of course he got there by teaming with Gil Reyes of the notoriously "well developed" UNLV sports teams of the 80's and early 90's.
Pete is the *best* answer to this question, since there was no question of either his level of competition, or of his training/transformation.
Roger would be by far the oldest man to win a *legitimate* grand slam level event, ever.