Short answer: No, it's dangerous.
Long answer: Dry ice expands at a very fast rate, even with a blow off (pressure release) valve, it can be overwhelmed by the expansion and blow up the keg anyway. Dry ice (when it sublimes into CO2) doesn't get absorbed on it's way out of the liquid (bubbling), so it is less efficient than just gassing the beer like normal. If you want to carb in the keg without a CO2 cylinder, prime with sugar like normal (though you might want to use a bit less sugar) and place at room temperature for 2 or so weeks.