Yes, it does. Some NM rifles were ordered with Lyman rear sights. Probably at least $200-300, but that is a guess. Pictures would help.
For the benefit of others:
--a M1903A3 barreled action with correct handguard and retaining ring, cannot be easily inserted into a M1903 stock without some fitting. The ring gets in the way;
--A M1903 will drop into a M1903A3 stock with no problem.