It will likely depend on how good the master recording is. Most of the earlier master recordings were done on film rather than a video camera, which means that if the recording was done with the camera in good focus, there should be no issue getting it remastered for HDTV. The only limitation may be the sound since Dolby Stereo was the closest they have to surround sound in the early days.
It will be a bit like getting photos on 35mm film coverted to digital on today’s equipment compared with that 10 years back. The quality of film has not changed much over the years, where as the process of converting it to digital has made a significant improvement.
The same holds true for music. I have been recently involved in getting professional sound equipment to set up a local recording studio for converting a huge collection of large Real audio tapes. I could not figure out why one of the requirements was 96kHz 24-bit MIA sound cards for their PCs to record from these 60’s and 70’s tapes until I heard what the sound quality was like. If I heard the audio only, there would be no way I would have guessed that this was coming from a tape!