Some pilots have been able to call ATC when their aircraft was doomed, the PSA 727 crash comes to mind as a good example. This was after the crew knew they had lost control of the aircraft and they had time to let the tower know. Every situation is different and every crew member is different, if you have time to let ATC know whats happening that's a good thing, but only after you have addressed the priorities as other members on this board have mentioned.
09:01:55 Captain (to Lindbergh tower) Tower, we're going down, this is PSA
09:01:57 Lindbergh tower OK, we'll call the equipment for you
09:01:58 Unknown Whoo!
09:01:58 ((Sound of stall warning))
09:01:59 Unknown Bob!
09:01:59 Captain (to Lindbergh tower) This is it, baby!