It's a neat idea, and it's not like this hasn't been done before, just in game. After all, remember the daycares? The number of levels your pokemon gained while under the care of the old man/old couple was based on how many steps you took, and in the DS series, you even got an in-game pedometer. So really, instead of just sticking a couple pokemon in the daycare center, and zooming around on your bicycle for a while, you could go out for a jog. Like, an actual one. And true, the pokemon will probably have not as good stats, but that's true of the daycare, anyway, right? I'll mostly level up the usual way (especially because the Gold/Silver games are the best in the series, IMHO), but when I want to quickly evolve a pokemon, just for the pokedex, or that creepy guy who liked looking at pictures of pokemon (the dude in the Kanto region, north of the Water Gym), I can just go for a run, and get it to level 30 or whatever (especially if doing this will make your pokemon like you more - thus, evolve quicker).
Really, this is just a cool way to do some real-world grinding, if you will. I just hope that you can transfer eggs to the device, because that would be really cool.