Naturalisation question

Sounds very unlikely. Not that he might not have a reason to complain if there was some kind of misunderstanding but in the end, the only thing that will generally count for the time of residency is from when it was made official. He can always plead his case if it is a question of qualifying for citizenship for example but I would not get my hopes up too high.  They would have to make a special exception and this will come down to a decision of a particular official, there is no way anybody can know with certainty how they will decide.

Not registering a residence is a punishable offense in Germany, as is living in a building not approved as residence.
Thus I recommend your friend keeps a low profile about this and only counts the time from after he lived here correctly in a legal sense.