No, an Ad Hominem is an argument against the man (well, person), as its name says. It's any argument that tries to invalidate an argument by attacking the person who said it. In fact, insults are not necessarily Ad Hominem fallacies, and the accusations don't have to be baseless to be fallacies.
I'll start by saying I think you're absolutely correct.
To further refine the point (possibly what you meant in your penultimate clause), it's not ad hominem when the attack on the man in question is germane.
If I say "I am a good candidate for US President", and you say "You don't even know how many US States there are", it's an attack on me ("the person", that is the arguer), but it's totally relevant, and thus not an ad hominem attack in the sense of the logical fallacy.
To bring it back to the case at hand, if someone says "Adria's wrong that it's offensive, because if she says that then she's a hypocrite, because she says offensive things", that's tu quoque (and yes, ad hominem). Murderers are not incapable of identifying other murderers!
But for one thing, ericb makes a good point that hypocrisy is suggestive that she might not have been genuinely offended, which plays some role in this story.
Moreover, hypocrisy plays a complicated and not-entirely-fallacious role in circumstances where we disagree about acceptable behaviour. If Adria's claim is that double-entendres are inherently unprofessional behaviour, but I disagree, one basis for disagreement is to cite community standards, and Adria's own behaviour seems likely to be behaviour that she will accept as not-abhorrent. She could argue "yeah, it was repugnant of me to do that, just as it was repugnant of this man to make a dongle joke", which would mean she was a hypocrite, but the hypocrisy would not affect her argument (unless some other part of her argument required her to assert that she's a virtuous person). Or she could argue that only privileged groups can offend (as she apparently has about racism, much as this argument disgusts me), and insofar as she was persuasive about this, she might evade the accusation of hypocrisy and also the impact on her argument.
I assert that it's a sign of mental laziness to hold hypocrisy as a great evil, in general. I think evildoers who think their transgression is evil are less evil than evildoers who think it's just fine and facilitate it in others. Even though the former are hypocrites and the latter are not. (And if, at some point, I accuse someone of hypocrisy, it will make the preceding statement by me no less true!)
