Adding always hot outlet to switch controlling fan
No.  If the line wire goes to the light box first, the wires to the switch from there are used as a line wire and a switch leg.  To add a receptacle at that location you would need a line wire and a neutral wire, so you'd need a 3 wire cable.  One option you may have with modern products would be to switch the light to a wireless switch and use the wires as line and neutral, all though that may give you nuisance concerns.  If removing drywall or damaging finish is prohibitively expensive, you may need to hire a Master electrician to pull a wire to a new box for you using a concealed work permit.