No.

Why should anyone care? Why does it really matter what a fictional or in the larger scope of things a real person's sexual orientation is?

I doubt it. At best he could be bisexual and even that I would doubt.

All his love interests had dongs all along!

There isn't anything in the game that would lead me to believe drake is gay. So no, it wouldn't fit at this point.

Wait, he's not gay? I always thought he was gay, or at least bisexual.

Nathan Drake has had relationships with two women so far in the game and zero of the men that hes come into contact with have had his sexual interest, so no. Its not about what could've been but what is. If he was created to be homosexual or bisexual then he would've been. Naughty Dog set the bar with lesbian love in the Last of Us DLC though. They are proving that they are ready to move forward to modern topics and the fact that a heroine could be a homosexual female with no interest in males.

This should be written off as just a fantasy, or alternative view because its not cannon. It he was written to be a gay character then it would be no problem. Who knows? Maybe they should try it in the future. 

Being a few paces away from Sully...who wouldn't turn gay?

considering that hes supposed to be married to elena then... NO!

plus he spent almost three entire games going after elena so again... NO!.