For me, I think that yes, that would be a deal-breaker. You've talked to him about it before and he hasn't changed. It's pretty hard to be worrying if your partner is ok because they couldn't have the decency to let you know what was up.
I know that you didn't ask about this part, but it also seems like having a partner who is out drinking all night might not be the best thing for you in early sobriety or in later sobriety. You will likely grow tired of having him being out doing that sort of thing.
It also sounds like alcohol could be playing a role in why he didn't text. He may simply have been too drunk to remember. Drinkers can be pretty unreliable and don't seem to make the best partners.
I don't know all the details of your relationship, but from what you've said here, it seems like the two of you probably aren't really compatible.