Yes, it would have destroyed his life and career. In fact, had he been openly gay he would have been ostracized in New Salem, derided in the military (remember he was elected an officer of the militia), and, I'm certain, never elected to the House of Representatives. In fact, he would probably have lived in New York or St. Louis instead of Springfield. And he certainly wouldn't have been nominated to the Presidency!

While it happened some years later, consider what happened to Oscar Wilde. Lincoln was living in a time and place where to be openly gay, or even if there were reasonably substantial rumors of being a "pouf" would have most likely gotten him tarred, feathered, and ridden out of town on a rail (if he was lucky). It certainly would not have helped his law or political careers!