Do they deny homosexuals entrance into the armed services?

If so, could one merely claim to be a homosexual to get out of being drafted?

In theory, yes.

However, in times of war (when there actually a draft), the army would want more than just your say-so. In the Vietnam era, they demanded some sort of proof (IIRC, there was one example where someone was asked to produce a marriage license to another man to get off).

Randy Shilts wrote a book about the history of gays in the military and the general pattern was:

In peacetime, kick them out.
In wartime, look the other way.

What’s worse: having sex with a man to avoid armed service, or blowing out your right kneecap to do the same? I’d probably do that latter.

Would a gay porn video with the draftee as the star be sufficient proof?

Recent thread on the subject:

What constitutes legal proof that one is gay?

Well then, in times of war, the draft board will have a special room where all draftees who claim to be gay are led to. Inside will be fuzzy padded table with stirrups, a male nurse, a cowboy and a leather clad biker. Go figure out how they get positive proof.

No offense meant, but you be sick, dude.