Hey there!
I’ve used the Web Books Viewer quite a bit, and I can confirm that it works just fine on Android devices offline. I’ve been able to open my EPUB and WEBZ files without any issues, and it doesn’t require the Chrome browser, so that’s a plus if you’re not a fan of keeping everything on your phone. However, when you’re offline, some features like annotations and bookmarks might not sync with other devices, but as long as you’re using it on the same device, you should be okay. I’ve found it to be pretty smooth overall, and it’s nice not to need a traditional installation.
Hope that helps!