She will be able to get emergency medical cover using her European Health Insurance card (the replacement E111 card). So if she broke her leg or had some kind of infection for example, she would be covered. If it was just something like a cold, I doubt she would be able to see a doctor using the E111.
I'm not sure about being able to register with a doctor though. If she was ill, I think she would just have to turn up at the doctor's or hospital and get seen to then and there.
Obviously, once she starts paying social security here, she will have exactly the same rights to healthcare as the Spanish.