I think Punk was generally staying in character. In the same interview, when asked about a possible match between him & Lesnar, he said something along the lines that Lesnar would be crazy to fight him. Given Lesnar's part time status in WWE, he's not going to be teaming with anyone. Given Lesnar's star power, Vince probably feels the tag team division is a waste of that. Truthfully, he's probably right. Lesnar is a hired gun brought in and used every so often to jack up ppv buys.
If they were to become a team, however, I see no reason why they wouldn't be a great team. They'd immediately be the most talked about tag team wrestling has seen in years. Punk & Lesnar are a great mix with Punk as the guy with the speed & skill while Lesnar is the powerful bruiser. Toss Heyman into the mix as the manager for their team and you'd have fans all over the net wetting themselves.
As far as a name goes, I think WWE would best market them as simply calling them "Paul Heyman Guys". That could sort of be their "unofficial" official name. In a promo, Punk could simply refer to himself & Lesnar as Paul Heyman guys, WWE puts it on a t-shirt and said t-shirts start selling like crazy. The fact that they both do indeed happen to be Heyman guys only makes it all that much more marketable.
As for winning the tag titles, why not? Brock Lesnar's first run in WWE is talked about passionately to this day. Lesnar's one of the most dominant guys in the history of the company with wins over many of the best that's ever been in the business while winning 3 WWE Championships along the way. CM Punk has only recently gotten off the longest World Championship reign WWE has seen in, literally, a generation and is one of the most over wrestlers on the roster. There'd be no point in putting two guys like them together without making them tag champs at some point.