I doubt that they will. In any other generation that had a large storage option of some kind, it still didn't seem to affect the amount of in-game storage available. I suppose that it may be different with X and Y since they're launching this service fairly soon after release, but I seriously doubt that's the case.
iirc, B/W had a maximum 24 boxes of 30 pokemon each, which is a pretty large amount of space for any purpose that isn't completing the pokedex. I wouldn't be surprised if they pushed it up to 28 or 30 in-game boxes for this one.