If you are able to connect to a noble family around the 1600' which gave ties to the kings of Denmark it's possible. Just make sure that you have good sources om every connection and don't trust what other peoples have wtitten but try to check the sources your self.
The oldest line of mine that I'm pretty sure of goes back to around 1280 and ends in Bohuslän.
Just remeber that genealogy isn't about getting most people in your tree, getting the furthest back in time or find your lineage back to famous people, but it's about who were your ancestors and their families and their lifestories, and trying to find the truth about this, by using as good sources as you can find.
And don't think you would like to present your family with a familytree that has false connections and has a lot of fantasies in it.
Try to be the best genealogist that you can be.