Feasible in a centralised, OS-level ad system, yes. iAds may do it, I have no idea. But most ad systems are embedded at the app level, so when that app is turned off, no downloading can take place.
You don't need it to be OS-level. When an app with ads turns on, just have it grab a whole bunch of potential ads and cache them in some shared data store (e.g. a Content Provider).
I imagine that the harder part is grabbing the right ads so that you have something relevant to show. There's also some concern about leaking ad information, but I'm not sure how much advertisers care about that.
You don't need it to be OS-level. When an app with ads turns on, just have it grab a whole bunch of potential ads and cache them in some shared data store
That alone would require it to be OS-level, at least on iOS (AFAIK).
You could probably do this with some cleverness using Keychain or a custom URL scheme that an app with ads will only respond to if they have some ads cached. I'm not 100% certain on this though as I've done very little with iOS.
On Android this is obviously much easier. Just use a content provider as I mentioned above.
I imagine that the harder part is grabbing the right ads so that you have something relevant to show. There's also some concern about leaking ad information, but I'm not sure how much advertisers care about that.