Does a postdoc qualify as post graduate? If so, yes. If not, then the answer is no.

To find employment, foreign nationals who have earned a Swiss university-level diploma will be entitled to stay in Switzerland for six more months from the time of completing their education or postgraduate studies. Those who are successful in securing employment will be issued a work permit, provided the prospective position involves an activity of particular scientific or economic importance.

https://www.bfm.admin.ch/bfm/en/home...abgaenger.html

Any postion will still need to meet the scientific/economic importance criteria too.