Depends on the situation.

The problem is that you're applying the legal justification for one circumstance in which drunkenness affects the law and applying it to a completely different legal concept.

For the victim, intoxication matters because it is a legal factor in determining consent. However, for the initiator of sex (i.e. the one who actively engages in the sex act), drunkenness is generally not a factor in determining criminality, because voluntary intoxication is not an affirmative defense for a crime. You can't get out of murdering someone because you were drunk, nor can you get out of a DUI because you were too drunk to know you shouldn't drive. The same applies here. If you actively engage in sexual intercourse with someone who cannot consent, you are guilty of rape.

This doesn't mean the man is always on the hook, which is why I said it depends on the situation. For example, if a woman climbs on top of a drunk man and initiates sex with him without his consent, she is guilty of rape, regardless of whether or not the man is erect. Because legally, arousal DOES NOT equal consent.