Yes, in fact, with Backgrounder you can control exactly how you want each app to be backgrounded. But even better, Backgrounder can enable native multitasking even for apps that don't yet support it! It's really quite nifty.
Here's what I've done:
1) Installed Remove Recents from Cydia. This removes all apps from the task bar that aren't actually using multitasking.
2) Installed Backgrounder. Set global multitasking to "Native." Now fast app switching is enabled for all App Store apps.
3) Created exceptions for apps like Clock, Calendar, etc. so that they never multitask.
If I want to fully close a native or App Store app for which I haven't created an exception (for instance, if I want to close Settings so it will start at the main menu next time it is opened), I just use a short hold to disable multitasking, effectively closing it.
If I want to background a Cydia app, I use a short hold to enable backgrounding. Note: I could set Cydia apps to background by default, or set individual Cydia apps to do so, but I prefer to manually control non-native multitasking, since it is so battery-intensive.
hmm. thanks for posting this. i was wondering what backgrounders purpose was now that apple had mulittasking.
for #3, what are some common apps besides the ones you listed that would have exceptions created for them?
also, should the apple messaging app be set to native or off? thx