No, it doesn't. That would be a U-turn move. The south end of I-295 in New Jersey is the only direct connection between the 295 and the Turnpike. New Jersey didn't want a free highway competing with the Turnpike when the I-295 was built, even though the two highways in some places are right next to each other.
If you are on I-295 south and want to get on the Turnpike going north you have to take Exit 2B (Hawks Bridge Road) go east about a mile and turn left at the second traffic light. Stay in the left lane and bear left at the first fork. Be careful, the sign directing you to the Turnpike comes just before the fork, it is small and hard to spot.
There are also several other indirect connections further north, at I-295 exit 11, exit 36, and exit 56 that will connect to the Turnpike via local roads.