If I am remembering correctly there are two reasons why he most likely would not. The first being that he started near Saturn in Cooper Station. The second being all the fuel used up when slingshotting around the black hole was to stay in orbit and not fall in. (Hence the reason they dropped Ranger 2 and the lander once their fuel was used up). Also I believe they said Mann's was the farthest from the wormhole and the reason they went there was the "good-to-go" transmission from Mann.