Eh, some mostly off-screened clashes between revos and BBPs over this plot point are definitely possible, but Dragon vs BB seems quite hard to imagine imo. Like, let's be real, no matter how much Oda stretches the manga, Dragon is gonna get like 2-3 actual fights, not more. And he's got a lot of good opponent options – all coming from the WG and the Navy (by that I mean Akainu in particular). For instance, it's easy to imagine his first fight being something needed to hype him – something like dispatching a Gorosei. Then he can have a skirmish with Akainu. Later down the line, maybe towards the very end of the manga, he can aid Luffy vs Imu in a grand team fight.
I just don't think it'd be very reasonable for Oda to make him fight a pirate when the established narrative (revos gotta deal the WG at least several major blows) all but funnels him towards fighting WG-related opponents.
Plus, Teach is already involved with another monkey – Garp, and we can't forget his involvement in the whole donuted-man shenanigans.