I think he did, in the following scenes Dath appears wiping his mouth
Yeah but he doesn't rub his mouth until after hos conversation with that other omega (I forget his name). It looked like he cake ans interrupted the two before anything happened. I would think if they actually kissed Daath would wipe his mouth immediately, but who knows.
He didn't do it immediately because he didn't have time to think about it. After the kiss everything happened fast and that was the first moment where he stopped to think about what happened
I don't think Daath and Will actually kissed though? They got close, but did their lips actually touch? I think Daath didn't reject will because there really was nothing to reject.