Unlikely. Most teams only require compensation for lateral moves, this is a promotion for him. If teams blocked their employees from taking promotions, they'd have a hard time getting quality employees.
It really isn't that big a pay raise. He turned down more money last year to come here where he had a better path to playing time (if I remember right). He had made 2.6M the previous year, so it would probably be better to look at it as 2.6M to 3.2M to 3.9M or something like that. We just got a discount in the middle.
Prince Fielder has a terrible body, but led the league in home runs one year, and is a career 300 home run hitter (so far). Maybe it's not on the same level, but judging based on body probably isn't wise.
It's too bad he can't score unless he dunks it (and even then only sometimes). The blocks and defensive presence are nice, but teams are likely going to simply ignore him offensively and double someone else.
At least one thing interesting about Happ is that he's been gaining velocity throughout most of his career (much like Lee). He probably isn't a guy who will lose a lot of stuff over the next few years.
It'll be really interesting to see how much Price gets. A lot of the players seem to get more than I expect, but I find it hard to see him hitting 30M / year. I can definitely see 7/175 or 8/200 though.