[ptaipale]

Not really. In the Nordics, the right to public healthcare comes with a residence permit. (And nowadays, at least in Sweden, to some extent even with illegal residency).

Of course, you may still want to have a private healthcare insurance to have quick access to care. The public system in Nordics is great for preventive care for children, and emergencies and serious situations for everyone, but not so great for everyday items. Larger employers often provide a private health care plan so that employees don't have to spend hours in queues.