Though I would still think that if this is the first time that an air force is going to be flying Russian fighters, they would need a lot of time just to integrate this fighters into service. And considering the maintenance levels and logistics consideration associated with maintaining a mix of aircraft from both sides (something we regularly faced here), it is still better to stick to designs from one side, not mix around.
Take Indonesia for example. Before the Flankers went in they could barely fly their F-16s at any rate, and the Flankers simply made it worse (in a lot of aspects, especially systems integration and the fact that they have nothing to fire with).
F-35s could probably still penetrate our airspace (there was a story about one of the test aircraft or something flown over SEA airspace, and Indonesia is the only one to make a full intercept because the rest knew what it is, or simply don't bother), but it would take a lot of effort to send them over (unless it is a carrier-deployed aircraft). No matter what, for long-range operations a tanker would still be needed (this is why our Fulcrums and Flankers have refueling capability).
JA 37 Viggen: Probably, but one can't simply jump into the Superbug and expect it to handle like a Hornet. It is a completely different animal (something like the Strike Eagle to the normal Eagles, except that the differences are far more pronounced, due to the new airframe).