Under the current Windows Phone 7 Application Certification Requirements (pdf) applications running under lock must "stop any ... active timers" (section 6.3.1). However looking out on Marketplace there are a number of timer/stopwatch apps claiming to run under lock and also allow lock to be disabled in their settings. How are these apps certified or is there some loosening on the restrictions by Microsoft if the app allows the user to make that decision?
Also some of these apps also suggest they continue even when the app is exited or when the device off. Is it the case that they are not truly running under these circumstances, i.e. the timers either start where they left off when reactivated, or perhaps use the OS time to work out the time elapsed between tombstoning and reactivation? In these circumstance I also presume it is not possible for the app to notify the user when the timer completes?
6.3.1 requires apps to offer the ability to prevent the app from running under a lock screen.
Apps can run under a lock screen by disabling ApplicationIdleDetectionMode.
You can keep track of time while the device is off using the OS time as you note. Peter Torr demoed this with tombstoning state in his WPH305 Tech Ed 2010 Talk.. refer 28 minutes in.
You presume correct that there is no ability to notify the user using client APIs on a timer. The closest you'll get to this is notifications which entails network communication and presumes connectivity.