To get cheaper health care? no. To get better health care? yes.
I live in the UK. It took six months of doctors appointments and referrals before they would remove an ingrown toenail. When I lived in the US I called a Podiatrist, got an appointment the same day, and had the same sort of issue sorted all in the same day. But even in these socialized medicine destinations like where I currently live, it is far from free (six months of pointless appointments and referrals costs a lot of money). People visit here, get hurt or sick, go to the doctor, then go home and they think it was free, which is the idiotic mistake people make in analyzing it. It costs the taxpayers here a LOT of money. I found it cheaper to insure myself in the US than the insured-through taxes burden that exists in Britain.