No, ratings don't change without votes being cast. But new posts automatically start out with a higher rating, so a post must grow its (positive) vote differential by 10x to "keep up" with the new posts. The rating increases as a log of the vote differential, so the votes need to increase exponentially, not the rating. The vote differential increasing by 100x would result in an increase of 2 rating points (this is what a logarithm means).
A new post submitted on June 8, 2008 would have started out with about 1753 rating points, and this number grows by a little less than 2 every day. So it's not that big to store.