Can I use this to deploy my project which needs some database connection?

Git is a software and doesn't provide any server. GitHub also doesn't provide any server for running your software but provides hosting for your Git repository which doesn't need any database. I guess you're either taking about GitHub pages where you can deploy your website or Github Actions where you can automate your build process. You cannot connect privately to a database from GitHub pages as it provides static hosting only. You can connect to database from your Github Actions script but it is short lived and timed out soon so I don't think you can achieve what you're trying to.