No, you can't. If you have a backup from your cloud slot you need a postgresql database server to backup to. You can install postgresql on your own system for development purposes. 

Check this very nice guide for the steps:

http://www.nolanramsey.com/blog/2015/5/29/how-to-use-your-mendix-cloud-database-locally

Be sure to use a non-secret password because it is possible to see the database password for every other developer in your Mendix project by clicking the show password checbox in the project settings.