I've had similar concerns about oxygen pickup when adding gelatin. It makes the beer super clear, but lately I've deferred to just putting more kegs in the conditioning fridge and letting actual time do the clarifying for me instead of using gelatin as "liquid time".
Without any empirical evidence, I'm guessing it's close to a wash. In my head anyway, the beers age better if I leave them alone, but taste better young if I fine them. Since I have the fridge space now I'll trade time for more work (at least until I find a reason to reverse myself).