The whole Archie cast of characters is reasonably well-known, I think, but uniquely in that long-running Archie house look, and in stories that always seem at least ten years out of date, even if they're brand new. That was kind of the bedrock of Archie comics for, literally, the last half century. There were some minor tweaks over the years, of course, but I doubt most people could differentiate between a Harry Lucey and a Dan Parent story, or guess within a decade when any given story was made. (To be fair, Parent made some significant progress in making the stories more inclusive, but I daresay anyone outside comics is very familiar with that. They might be able to recall something about introducing a gay character, but I doubt their knowledge goes much further than that.)
So even though the Archie line was completely revamped in 2015 and there's a new live-action TV series set to debut in a few weeks (with all the accompanying promotional hype) I don't think the vast majority of people realize Archie isn't the same Archie that he's always been. So when Nate refers to "the old Betty and Veronica", I don't think most readers would get that. Betty and Veronica haven't changed in 50 years, as far as most people are concerned, so "the old Betty and Veronica" doesn't make sense. If the character were referring to "the old Batman" or "the old X-Men", I think most people would understand that the characters have changed over time, and the gentleman prefers the version he had as a youth. But Archie was so specifically immutable for so long, I don't think the joke works for Big Nate's primary audiences: newspaper readers and kids who pick up the collections in bookstores. The comic shop audience that would get this joke likely isn't reading Big Nate. It's not that the joke isn't funny; it's just that it's for an audience that I don't think overlaps much with Big Nate's.