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.
Honestly, in my state (Australia), the hospital system is crumbling because people are going to hospital for minor shit that could easily be treated at their GP. The amount of ambulance ramping at the ED is crazy. People are waiting 6-7 hours after being taken by ambulance to hospital. People often die because they are being ramped. A stroke victim died recently here because they had to wait like 5 hours, and the stroke killed them.
edit: I misread the question, sorry.