Picard was born in 2305, and (I believe) Kirk first took command of the Enterprise
in 2265. I can't find anything on when Jean-Luc's father, Maurice Picard, was born, but just based on Jean-Luc's year of birth it's doubtful his grandfather was still in diapers by the mid-2260s. Possible, but probably not likely.
Still, I think it's just best to not take the line literally. I highly doubt Kirk knew exactly how old Picard was when he said that. He was just saying that he'd been in the business of saving the galaxy for a long time. But when you think about it, that doesn't really mean much since he'd spent the last eighty years in the Nexus, during which Picard had amassed nearly forty years of experience as a Starfleet captain himself.