score:5
Yes, it is allowed. I base this on the lack of a law forbidding it. The chapter in the law about specific requirements on foreigners is rather short (chapter 2 in utlänningslag). Regarding work I only find:
Arbetstillstånd är ett tillstånd att arbeta i Sverige. En utlänning som skall arbeta i Sverige på grund av anställning här eller utomlands skall ha arbetstillstånd.
A work permit is a permit to work in Sweden. An alien who is to work in Sweden due to employment here or abroad must have a work permit.
Looking for employment is obviously not employment.