If a user gets question banned after asking a new question but that question then gets migrated to another site, is the question still taken into account when calculating whether the user has a question ban?

I remember that I asked a question on an SE site and I immediately reached the limit - it didn't matter if it was upvoted/answered. In my memory, the first reactions were positive including a couple of upvotes, maybe even an answer. The question then got migrated and the "ban" was immediately lifted (as opposed to having to wait for a couple of months for it).

The Question ban FAQ states:

Additionally, for question bans, the fact that a question is deleted counts against you, if others have invested time into answering or moderating the question.

Migrated questions are deleted - does this count against the user? My memory of being unbanned seems to indicate it does not but it's not clear.