Space Engine doesn't simulate star motion within the galaxy, so this isn't possible.
It's a good thing it isn't based on star motion then, because it's really neat to watch.
Yes, it is caused by precession of Earth's rotation axis.
Just checked it out myself; turns out that Vega never gets very close to the pole so it wouldn't make a great pole star. The only bright stars to get very close to the pole are Polaris and Thuban.