Never used the App Image, it’s was against my religion 🙂
Without the App Image you might encounter few issues depending on your DE (Desktop Environment).
The less annoying one but I never figured it, was issue with the icon of the app in KDE and LXQT, but it was fine with Gnome.
The most annoying was again in KDE and LXQT was issue with the key chain which was not storing password of the Publii. In the mainwhile the team and I figured it and they flagged Gnome Keychain as a dependancy.
Otherwise, it was running pretty smoothly like it is on Mac and Windows.