It's more likely that permits are used to estimate population growth. That said, the estimates were noticeably wrong with regards to some states. Alabama, for example had a population estimate for 2020 that was over a 100k under the census count, and while the census number was within the margin of error in the follow up survey (which also basically knocked out all of NY's 2010-2020 population gains), it showed that the census count in Alabama leans more towards being an undercount.

That said, part of it might be that the requirement a permit to build house in Alabama might be a little loose in parts of Alabama. I don't know if you need one in Bibb County, for example, and that's part of one of the biggest metro (albeit the most rural part of that metro).