No. The code would need to be modified by the Itch team on their end to recognize certain extensions (.x86_64, .appimage, etc) to tell the Itch app how to install them. So far the extension file in the repository has remained untouched for 5 years, so it's very unlikely this will be fixed any time soon. The code can be found here
The dev should be able to get around this by zipping up their game before uploading it to itch.