Yes it is possible. Is it very likely or provable, no probably not. Here is an article by Lars Loberg a respected Norwegian Genealogist that is worth reading before you begin your search.
NORWEGIAN KINGS AND VIKINGS DO THEY BELONG IN YOUR FAMILY TREE
A major reason for the difficulty lies in the lack of Norwegian records from before the 1300's a time of great death in Norway due to the plague.
It is possible in many cases to trace your Norwegian ancestors back to about 1600 and in many cases several ancestors can be found. Sometimes one can get lucky and due to some old parchment records having survived you can go back to around 1400. But past that with any certainty is very rare indeed.
Norwegian parish records on Digitalarivet can take you back to the 1700's and in some cases back a little further. The various Bygdebøker for some parishes and some farms can go back into the 1600's and occasionally a little further. But back to the Viking era of 800 to 1000 AD is difficult with any degree of certainty.