I've read extensively on Lincoln and have heard of the possibility of his having had syphilis. What treatment did he get that could have caused his depression, though? I'm not sure how they treated syphilis then, assuming he even had it. There's no doubt he suffered from depression; it's also possible he was bipolar.
There's so much speculation about every aspect of Lincoln's life. One book suggested he was gay, or at least bisexual. The evidence was pretty flimsy.
As for your question, I guess I just don't know, and I'm not sure it matters. I personally think Lincoln's depression came from his great intellect and ability to think deeply. It's hard not to get depressed if you do that.