If you import a backup file done with this plugin, first old data is deleted and then import is performed. Merging old data with the new would lead to many problems (duplicate questions/users, non-unique id's, etc). So the answer is unfortunately no.
If you wish to move your database to another server, you can do it. The only thing you need to change manually is to update your site url in Admin->General->"URL to use when referring to your site".