I think that trading Eddie House was made more with an eye on the long-term rather than short-term. For this season, the trade was potentially a wash, but Ainge would have more options for the future.
If Nate Robinson has played well, the Celtics would have had the non-Bird exception and could re-sign him for a contract over the vet minimum without dipping into the MLE.
Regardless of how Nate plays, I think Boston can still do a sign-and-trade with Robinson, which means that a team that wants to do some creative salary cap finessing may want to acquire him in a way that doesn't use any cap exceptions, the way Ainge fruitlessly sought to get Marquis Daniels without using the biannual exception.
If Nate Robinson doesn't play well, then Boston isn't tied to him beyond this season and can wave goodbye.
The trade didn't do much to make Boston a better team for this season, but it did give the Celtics a better chance at getting younger (Nate is 26, House 32) and more athletic, either by Robinson showing himself to be a valuable bench player or by upgrading the trade assets in Ainge's arsenal. I think it was a reasonable gamble.