Most probably! Check out the section that has the Gloomhaven pic and the SPECS section right below it. Many games are listed here with more in the wiki list which you can access by clicking the Gloomhaven pic.
Backpack Main Compartment Inside Dimensions:
16.5"H x 13.75"W x 8.5"D
42cm x 35cm x 21.6cm
16.5"H x 13.75"W x 12.5"D
42cm x 35cm x 32.75cm
**Keep in mind, although the specs list the internal measurements as being 16.5" high keep reading the info on the main campaign page where we explain how longer games can fit if you move up the floor to the top section.