Yes. Well, I was thinking to store the stars galaxy wise. In the beginning not even all the stars but the closest ones. Currently the distance data is way too inaccurate to even those behind the milky way core not mention other galaxies (we actually cannot see many of them behind the clouds around the core). So I wasn't even dreaming about other galaxies. Of course this would get constantly more accurate as you travel to other stars and the distance/location data becomes more accurate.
The expansion of universum can be seen well between galaxies, but in a single galaxy the stars rotate around the galaxy core mainly. Sometimes their orbits may be altered by nearby objects (like other stars and black holes etc) so the database would require some occasional updating. But same way you need to update normal maps.
About to find out where you are: There are things you can measure. (let's assume we know we are in the same galaxy) The distance and direction to galaxy core (huge margin for error if it is far). The finger print for nearby stars and their positions. With those you could limit the search to database, but there is at least one problem. There are 200e9 stars in Milky way, so we need lots of storage capacity and computational power to process such amount. If you dream to keep all of them, some kind of automated data input/update system would be needed.
It is indeed easier to know where you are and just aim for the target system and let the auto pilot keep the heading. But I think the idea was to have some kind of general map.