[Edit: I think I misunderstood the point of your question:]
If you have an error handler set up to handle the error then it shouldn't throw up a popup alert in the debugging player. That alert comes up as a result of unhandled errors (I think - can someone correct me if I'm wrong?). The upshot is that you might get errors that don't throw up an alert if the AS3 code knows to look for them.
[...original post follows]
Flash Player 10.1 (currently in beta) allows you to define a global error handler. In theory, this should allow you to listen for all errors that may crop up at runtime and handle them quietly, without generating an alert window in the debugging player.
If you're interested, the 10.1 beta is here: http://labs.adobe.com/technologies/flashplayer10/
Let us know if that works out for you! :)