Yes, this can be accomplished through the SolidWorks API.
This is done often to push data from SolidWorks into various other systems within a company.
Give more detail on your database. Is it Excel, Access, SQL or ???? What type of data do you want to transfer? Do you use SolidWorks custom properties?
If you post your query in the API sub-forum the folks there can help you out. You should be able to hire a consultant/programmer to code what you need.