According to the canonical post on automatic bans:
Yes, ... deleted answers count towards an automatic ban.
Now, this is not very specific, and I suspect that is intentional. However there are certain cases where I don't think it would be fair for deletion to count against the answerer, and would love to see some clarification / guidance (without revealing any specific details about the algorithm):
answers that are deleted because the question was deleted. This was mentioned here, but no satisfactory answer yet. This typically will be through no fault of the answerer or any issues with the quality of their answer (though one could argue that a question that gets deleted should not have been answered - but then you get into whether the question was self-deleted, was it down-voted first, or did the community/moderators delete it).
answers that are self-deleted. For example, if I answer a post and then realize someone beat me to the punch with an identical answer, or perhaps later someone posts a better answer. This is peripheral to this recent discussion and again is not necessarily a quality issue with the answer or the author. In fact, we probably want to encourage, rather than punish, behavior that cleans up redundant or lower-quality answers.
In either case, I would hope that just the mere fact that an answer was deleted does not count against a user. In these scenarios it would be unfair, IMHO, unless the answer was down-voted or maybe flagged prior to deletion (meaning there was a problem with the answer, according to a user other than the author).