Eh, at my hospital I'd say the dietary aides got a decent amount of patient interaction. There was a menu just like in a restaurant (and it had a lot more than jello on it) and many of the patients needed help reading through and picking what they wanted to eat the next day. That could easily entail 15 minutes with particular patients every day. Then once the food actually got delivered a lot of the patients needed help getting their table set up, getting pop cans opened, putting the milk in their coffee, etc. The dietary aides would often "walk in" on a doctor-patient conversation, or a mobile test like the ones I was running, and get little glimpses of what goes on day to day in a hospital.
So I think it would be helpful in terms of spending time with patients - on about the same level that volunteering to play board games or whatever with patients would be. You wouldn't see much actual medicine occurring, but you would get a sense of all the different things going on in a hospital and get to see all the different wards every day. Now I'm not really sure with what exactly the OP is wanting out of this experience or what med schools are looking for... vet experience is a lot more hands-on because we don't have the same laws restricting us. But I hope I gave a good description of what the job would be like in my particular hospital that I worked at.
Another benefit that I think is important is that it is easier to get "better" jobs in a hospital if you're already in the system, both logistically and because you get to meet the right people and know who's hiring (there is a lot of elevator conversation in hospitals). So this job could lead to a more advanced or clinical one.
Oh, and the dietary aide is the ONLY person the patient gets excited to see, I can tell you that. Yes, they usually want to see the dietary person with their food much more than they want to see the doctor.