Yes you could just like today. There are some misconceptions regarding medical treatment in EU countries. As a citizen of an European country you are entitled to receive only emergency care in any other European country in the same conditions as the other country's citizens. You can't receive extended care without being a resident. Up until the recent economic crisis everybody closed the eyes to several things, medical treatments included. Spain is one of the countries which treated everybody irrespective of nationality, either from another EU country or from somewhere else. In fact, Spain was a destination for health tourism with even Americans going to Spain to receive free medical treatment. With the crisis several governments (the Spanish one of them) went back to the library and started reading the exact wording of the treaties, curbing what they used to provide to others in strict accordance with the letter of the Treaty of the European Union.

When in the past, in order to live in Spain, you just had to go to the police and register, now, you are able to register only if you have a job or, if not, if you show evidence of being a person of independent means and a full health insurance policy with full coverage. Otherwise you can not register as a EU resident. This has always been the wording of the treaties. You can go to look for work in another EU country for a maximum of 90 days. After that you either have a job and can stay or you do not and have to go back. Before the crisis nobody really minded this but now several countries do.