This question seems to be the essence of several others on this forum. I believe that it is possible for the active iPhone application to continue running, and specifically, to continue receiving timer call-backs, after it has entered the inactive state (either through the idle timer kicking in the screen lock, or through the user pressing the hardware lock button).
The documentation specifically says that while an application is inactive, it is executing, but not dispatching incoming events (I'm not giving a link because I'm jumpy about NDA - should I relax about that? Is this whole post a breach? sigh).
Also, two answers by user "Ambr Str" directly state that it is possible to continue receiving timer call-backs, and he supplies a snip of code to achieve it (I can't link to this because I'm a new user, sorry - search for the question: "What happens to an iPhone app when iPhone goes into stand-by mode?" to find his answer).
I've tried to create my call-backs as he suggests, but once my application becomes inactive, the call-backs cease firing.
I've just noticed that while the iPhone is plugged in, if the application becomes inactive (due to idle time out or me pressing the sleep button), call-backs do continue to occur - perhaps I should get my users to carry a battery pack with them ;-)