LizzyM has a quote that runs something like.. "If you can smell the patients, it's a clinical experience".
As for being worthwhile, I would say yes to an extent. When you apply to medical school, you'll list the number of hours you pushed the cart. More hours translates to higher chance of interview. There may be better ways to spend your time, but there is at least value in that activity for you.
You can be the judge of whether the patients value your efforts.
Yes, it is also a potentially meaningful experience. Do what you can now, be dedicated, and eventually move on to more prestigious volunteering activities such as what would be considered leadership roles.
You are getting face time with the patients! You are getting to speak to them! With any luck, they are speaking back. (In my youth I read an entire hospital menu to a man who would not respond to my questions. Finally, a nursing sister took pity on me and explained that the man was aphasic (mute) due to a stroke. She also schooled me on what he could or couldn't swallow. Was a good lesson in humility for LizzyM.)
Just being on the floors will give you the opportunity to see things and hear things that will give you a sense of what goes on. This can be a very valuable lesson.
And it beats cleaning gurneys and other activities that don't involve face-time with patients.