Nope, they totally rebooted the character. See also: Misogynistic, grim Pike becoming a warm father figure in the movies and Discovery.Well, agree to disagree. The Cochrane we see in "Metamorphosis" is a modest, moral man who is so proper he's initially horrified when he learns that the alien Companion is in love with him. The Cochrane we see in First Contact is... not.
Good movie, but the characterizations don't really seem like the same person, even accounting for the difference of several decades.
Supposedly they planned at one point to make Cochrane female for FC. That would have been like the recent Yeoman Colt thing (she's gone from human to spikyfaced alien) to the 10,000th power.