That's a large collection—is there a quick and easy way to see if the specific newspaper you're looking for is part of GenealogyBank's archive?
The answer is yes: both newspaper collections, displayed on GenealogyBank's home page, have a "view title list" link that will give you the information you seek:
Clicking on either link takes you to the master Title List; this is alphabetically sorted by state and then by newspaper title:
Note that each state is presented at the top of the Title List as an active link. Just click on the state you are interested in, then scroll through that state's collection of newspapers to see what titles are available. The Title List also shows you the date range for each paper in GenealogyBank's archive, and which of the two collections—Historical Newspapers or Recent Obituaries—contains that title.
Have fun searching—and good luck with your family history research!