oh hell no.
TOS Metamorphosis--
Kirk: You say this Companion found you and rejuvenated you? What were you doing in space at the age of eighty seven?
Cochrane: I was tired, Captain. I was going to die, and I wanted to die in space. That's all.
Spock: True, his body was never found.
Enterprise Broken Bow--
Forrest (in 2151): Rather than quoting Doctor Cochrane, I think we should listen to his own words from the dedication ceremony for the Warp Five Complex thirty two years ago (2119).
The dialogue and the math all point to Zefram Cochrane being born in 2032, meaning he was 31 in the 2063 scenes of First Contact.