I'm hardly authoritative on it, but it occurs to me the answer is no,
because you can't see another App's memory from your sandbox.
You could see it in logs if it was an App that regularly crashed is about all I can think of.
You could probably do that jailbroken too though.
You can actually search for "rooting",
and it takes a few results for it to mean something else
On the PSP you could write a program that launched another program.
On that platform the second program could have been angry birds,
and the first program could be a dummy launcher with the original
Angry Birds icon and a built in timer.
I think a jailbreak app could do that, but there'd be a less technological way,
like checking the battery level from start to finish of the day or something.