That's a great question (although I think any team could be inserted in the place of "Iowa" and the response SHOULD be the same). Personally, I would be to some degree. I've always been a Team Guy, period, no matter the sport, while acknowledging wrestling is a little different kettle of fish (you're on your own, but your points are being accumulated for Team results).
That said, Snyder's situation is pretty unique, but not unprecedented. And to my knowledge he's the first to miss a regular season dual meet to compete in an international event in a non-olympic year, not redshirting, etc. (that could be completely wrong, I don't recall any others but that doesn't mean it didn't happen).
Point being, if his choice is that he can do both and he's allowed to, he'll do both, but if he can only do one he's picking Freestyle internationally, then I'd have to really think about if I want him on my team or not. And try to not to let the fact he's a great wrestler that is sure to help us impede my thought process. Really, how good he is should be a secondary concern (I know, the real world doesn't operate that way - if he's great it's fine, if he sucks - bye-bye).
Honestly, at this point it's almost like a hired mercenary, come in and show up when we need you, we'll let you know when that is. And all of that is because he's awesome at what he does. I have little doubt there is some friction caused by this, there has to be.