I kept running into the one on Route 4, and the first time I re-battled her, I was a bit confused. I kind of looked at my screen and thought, "Um, didn't I already battle you...?" And then I kept doing it because I kept forgetting about her and I ended up yelling at my DS, "LEAVE ME ALONE!" XD
But I think it's a neat little feature. c: I haven't re-battled any others, but I should try to remember to sometime if I ever need somewhere to train my Pokémon if I start to get sick of battling wild ones.