They will have natures and IVs because that's an integral part of the Pokemon data. The IVs are probably mediocre to avoid the game being too difficult.
However, Joey's Rattata in HG/SS and earlier games is specifically programmed to have near-perfect IVs. Hence he always says it's in "the top percentage of Rattatas".
Most of the regular trainers don't have EVs though, they act like "just caught" Pokemon. I believe some of the more difficult trainers like the Elite Four do have some EVs to make it more difficult. And by that time in the game all your Pokemon should have naturally acquired all their EVs.
The bottom part means yes, because they keep it as if they are "recently caught" instead of fully EV Trained.