I'm always compelled to weigh in on these topics since I'm an SLP and gained great insight into swallowing problems as a result of my own treatment.
First off, has he had a modified barium swallow study (MBSS), when and what were the results? The MBSS is THE BEST ASSESSMENT POSSIBLE of swallow function as it allows us to see the muscles of the throat as we swallow - shows us if small amounts of food or fluid have the potential to leak into the lungs (called aspiration) Aspiration is dangerous because it can cause recurrent pneumonias - if the aspiration is especially bad then the prognosis for resumption of oral intake might be poor - if the aspiration is in small amounts then there may be the potential to strengthen those muscles so that his risk is reduced - Vital Stim is a very good tool for strengthening those stubborn throat muscles - however - it's use with head and neck cancer patients is somewhat controversial. I'd explore that more if your husband is a vital stim candidate before he actually begins.
If the problem is that he can't control the food or fluid in his mouth to get it ready to swallow, then oral strengthening and coordination training may be very helpful.
Since he's having trouble spitting then I assume he's having oral strength and coordination issues - depending how much his anatomy was changed by surgery and/or radiation then the oral muscles usually respond well to therapy. If his therapist has recommended oral exercises then he should be doing them several times a day! I got myself a little mirror and did them as I sat or even laid on the couch. Now that I'm up and about, I do them in the car as I'm driving.
Bottom line - his potential to eat again is very much dependent on the results of an MBSS- even if he aspirates he still may have potential - there's a lot that can and should be done for treatment before he accepts that he will never eat again. Be sure your SLP has a good amount of experience treating swallow problems - there's a wide range in clinical skill and it sounds like your husband needs a REALLY good SLP.
Please let me know if you have any questions!
Good luck to you both -I'm hoping for the very best!