The answer to your question is a definite YES but there are some problems which can occur.
The main problems are with the upper denture-I'm assuming we are talking about full upper and lower dentures.
The front of the upper denture usually has a flange which goes up to cover the upper gum and in order to make the denture stay in place this has to be air/water tight otherwise the suction is lost. The rim of a trombone/baritone mouthpiece is just the wrong size and causes the denture to rock and lose its suction-usually accompanied by the unrequired sound of castanets
Also when working the muscles which control the embouchure there are times when ligaments at the side of the mouth-you can feel these if you put your tongue up towards your cheek-bones between your upper molars and your cheek- force your denture down-cue castanets again
The solution is to use a denture fixative powder or paste which will work well.
If there is not a total loss of teeth then a partial denture can be made to work using clasps or other attatchments.
However the most satisfactory method is to fix the denture using implants. These are very expensive but very good.
You will probably have guessed that I am speaking from experience and spent 10 years visiting a local University Dental Department trying to get things sorted. They tried allsorts of different ideas including special magnets, incredibly accurately fitting dentures, 2 sets of dentures- one for eating and one for playing. Eventually, they tried implants and, after much intensive work, they were fitted. It was a Friday afternoon and next day I was doing Bass Trombone in Verdi Requiem. Imagine my relief when I got home to try them. They worked
and the concert went very well, much to the amazement of the other brass players
They are still working 7 years later. No problems.
Good luck to your father. Tell him not to give up-I'm only 62 and still going strong on alto, tenor or bass.