FWIW, JMHO, and all that, I'm thinking these guys are for sure riding much farther than the OP is used to, and very likely going faster, plus, they're riding road bikes versus his (heavier, slower) mountain bike. He's kinda gonna be the odd man out, on several fronts, so what's really the upside here?
If the OP tucks into this group, he's likely to be busting his hump just keeping up, and not likely to ride but a few minutes with them, and I don't think he's mentioned if he has any experience drafting and riding in a cohesive group.(yes, I know, you gotta start somewhere, but on a mtn bike dressed like a skateboarder may not be ideal).
That being said, if it's just a group of recreational riders, not an organized team out training, then I wouldn't call it a faux pas for the OP to just tuck in behind them and ride a ways, without actually getting permission. If they're like most group riders, they meet someplace, and whoever shows up, shows up, and they hit the road. It's not uncommon for regular riders on these things, to intercept the group at some point it's convenient for them, and then peel out of formation, the same way. Most of the Sunday club rides I used to do, I'd catch them 6 miles into the ride, and 70-90 miles later, would leave the group at the same point.
So unless these riders are particularly cliquish (which, unfortunately, a lot of "serious" cyclists do seem to be) it shouldn't be a problem for the OP to just tag along, assuming he observes proper group-ride etiquette. Besides, if they don't like you, they'll just drop you like a bad habit !