Many people say yes, and no. After Ben cut the cable and falls to save Jake, he is not seen resurfacing. Jake then narrates that the Coast Guard conducted one of the largest searches in Naval history, but to no avail. Weeks later, Jake saves a man who constantly asks where his companion is. The man explains "He never let go". This is implied that Ben's spirit perhaps lives on to rescue men left behind at sea.
There is another ending where Ben does survive.