Rockwell International, lead contractor for the Shuttle, at least had a database which stored vehicle configuration data. "Space Shuttle Technical Conference" (warning, giant pdf) refers to this when discussing manufacture of the tiles.
The Rockwell master dimension engineering data base and vehicle
configuration coordinates were converted into computer tapes that
drove the numerically controlled mills that machined the tiles to
(page 1070 of the linked document)
Contemporary advertising in Computerworld magazine mentions the database and computer simulation applications used by Rockwell, but does not refer to any CAD-CAM systems.
An unsourced statement in response to a quora.com question says the company was transitioning to CAM at the time, but drawings were done in the traditional manner.
When I worked for Rockwell, they were preparing for computer
controlled/aided manufacturing (this was pre-AUTOCAD so they were
developing their own formats, this was before I seriously got into
programming, I was shown the machine but can’t recall the hardware). I
drew on company coated Mylar, so I’d expect to see NAR Rockwell logos.
So, it's difficult to find a definitive answer,but it appears that CAD-CAM wasn't used, at least in the early design days, but that the design information was entered into a large database ("Completed designs are stored online").