Over the years, this has been a common question when I'm out showing homes. The short answer to this is NO. Let me elaborate a little on this.
If you are purchasing a home that was built at the turn of the century (1900's), more than likely there are no closets in the bedrooms at all. In those days, closets were not a thing, and people kept their clothes in a chifforobe. So, in this case, an appraiser will count the rooms as bedrooms. The home meets the standards of the time period.
For verification, and to make sure you get the correct information, I consulted with a local appraiser about this question. He advised that for the most part, they only count bedrooms with closets in them as bedrooms now days. The exception to this is: If you have a room that is of decent size, that has an exit in case of fire, they may count it as a bedroom. However, that is up to the appraiser doing the appraisal.