it wouldn't be impossible. If there's a contest in the same city as a gym, and Haruka has all her ribbons (or wants to be like Shuu and just skip a contest), Haruka and Satoshi could get into another arguement on normal battling vs. contests, resulting in them each making an attempt at the other's field (I wouldn't expect them to succeed, though probably do pretty well for themselves). See, the problem is that contests are only there for a limited time in certain areas, and I don't really see Satoshi going against Haruka in one of them (he wouldn't be as easily motivated as Takeshi was), so there'd need to be some reason to have Satoshi participate in one and not Haruka, with the previous example being the best I could think of. Gyms, on the other hand, are always there, so there'd be no consequence in Haruka participating in one before Satoshi does.