It's very possible that they'll do something like this, if they're as serious about "rebirthing" or "evolving" the series as much as they claim to be.

The main question is whether or not the idea can be improved, and if so, how? What would make it the best for the series, and - if the idea WERE to be sent to them - most appealing to GameFreak?

Edit: Actually, I was thinking there's another way it can be improved. A lot of the other "new features" included in the Pokemon series aren't very well-known, especially earlier in the games, which leads them to be poorly known overall.

However, if the game mentions the new features throughout the storyline... that's a different story. What if the opening of a ninth gym in the region was an ongoing plot-point? What if there was a character that mentioned a contest or something like that where you might compete for leadership of this new gym, and they commented on your possible candidacy as you progressed through the game? Suddenly, it's made fully clear that you get to do this, and it actually becomes a major goal in the game.

I think the idea of training fellow gym trainers is pretty neat.

It would actually be pretty neat if you could pit your gym's trainers versus another gym's trainers too, enter them into gym-only tournaments, perform guild missions, etc.