No, EMT does not "replace" hospital volunteering. They are completely different experiences.
Some schools do give you extra points for "volunteer" work on your application irregardless of what the experience was.
However, I recommend if you want to be a doctor then volunteer in the setting in which you will be working ... ie the hospital or a clinic to see what your actual life will be like and make connections.
Volunteering as a EMS provider is a good for someone who wants to become a paid EMS provider ...
I think your time would be better served in hospital work or in research.
But, there is nothing that says you can't do a little of both. If you enjoy EMS then great go ahead, but I still suggest you spend time in the hospital or a clinic.