You can, but then the rest of the function is pointless. Why would you update the contents of the <div> only to reload the page?
Here is my idea of how you want this to work:
Page is requested
{server-side code}
Select control populated from database query
Page is displayed
{client-side code}
Select control is updated
Form is submitted
{server-side code}
Database query is constructed from form data
...
Then something is presumably done with the returned record
Without the rest of the code, I really can't help any more than this.