Mass edit posts after importing

I’ve imported my posts from an old blog to a new database (wordpress to wordpress), and it messed up the categories. Some got multiplied with 0 posts in each category, some posts seem to have lost its categories. So I deleted all the categories with 0 posts, and wanted to mass edit some posts to those categories. I only have a question: Since some posts have several categories, will those be lost if I mass edit them to the same one? Say, if Post1, Post2 and Post3 are in three different categories and I’d like to add them all into another one, will they all be moved to the last, or will they have both the new and the old category?

Sorry for the horrible explanation.