Could a P-3 Orion fly off a carrier?
Well, going beyond just judging from the Electra's itty bitty stubby wings, digging around for Electra performance data I found a page that gives a takeoff distance of 1290 meters, or 4200 feet, which would most likely be the distance at sea level, standard day, max gross.  Which is what I would expect with such itty bitty stubby wings.

Even allowing for more power in the military versions, I'd say it's safe to go with no.