Sounds a bit like Mystery Dungeon. Altho it would be a good idea. Are you listening to this Nintendo?
No
I didn't really think about the plot too much but it's not supposed to be.
And just as Cooltrainer_Mike said it could have puzzles and things like that in it. Yes, it would have battling in it, and it won't be like a MD battle style, it'll be like the regular pokemon game style. You'll be able to see the pokemons stats.