Generally, it is possible to add any type of user controls to Sitefinity. Database or no database, the user control is still a user control. So, the short asnwer is yes- you can do anything with the user controls (and custom controls for that matter) in Sitefinity. Sitefinity provides you with the presentation layer, and with out-of-the-package functionallity you can still achieve a lot.
However, Sitefinity does not solve all possible problems a user might encounter. I would recommend you to get aquainted with the Dev Manual
You should have in mind, though, that if you mean simple persistence, Sitefinity will do that for you automatically, and you needn't worry about it.
the Telerik team