I could see it going either way.
With free access, people would be more inclined to go to the doctor for simple and small things, but in return would probably catch more serious issues early and have better access to treatment, therefor reducing the need for intensive and specialized healthcare.
Without, people avoid going to the doctor for small stuff, but end up having to go in with more complicated issues later on.
Living somewhere where the healthcare is not free but heavily subsidised people do not go to the doctor for minor issues because when I tried to call and book an appointment I got an answering machine telling me that they don’t have time to answer the phone today, try again tomorrow. And of course the online booking did not work.