Hmm, I can think of a way, but I don't see why you would want to do this.

CGI::Carp does its fatalsToBrowser magic by setting $SIG{'_DIE_'}. You could conceivably set $SIG{'_DIE_'} back to do nothing each time you go into the module, and set it back afterwards, but I have no idea whether that would work at all.

If I get some more time tonight I'll see if I can rustle up some example code.