No. You can imagine the fabric of space being dragged into the black hole faster than the speed of light. Since nothing within spacetime can move faster than that, no signals can ever leave the event horizon.

It's like a swimmer going over a waterfall. The water is like spacetime being dragged towards the black hole, and the swimmer is an object moving within spacetime. If the waterfall is falling faster than the person can possibly swim, the person can never get back up the waterfall.

For more info on this "river model" of spacetime, see:

http://jila.colorado.edu/~ajsh/insidebh/waterfall.html

http://arxiv.org/abs/gr-qc/0411060

Relatedly: Since spacetime can "flow" faster than the speed of light, you might think this allows FTL travel. Indeed, this idea is called the "Alcubierre drive".