i would like to be able to retrieve results from this search by connecting directly to their database instead of screen-scraping:
would it be possible to return the results programmatically into some variable, instead of manually doing this search and then going through every page to get the results?
If server provides such direct access, probably you may. For example, via SQL TCP/IP port.
But much more often used and best-practice way – via web service search/get methods.