I don't know how many times this needs to be repeated: Only if the app supports that. If an app does not support synching, that's not going to work for any documents created with that app.
Not necessarily. I use Good Reader to sync docs between the ipad and Google Docs (which is free). Good Reader gives you the option to open the docs in Good Reader, or other compatible apps installed on the iPad. So, and Excel file can be open in Good Reader, or Pages. Same for Word or PDF docs. So, you are not just limited to Good Reader for accessing docs.
Sigh. What do you think
'if the app supports synching' means? It means exactly what you call
'compatible apps'. Yes, you can sync Word, Excel, PDF, TEXT and some other document formats between certain apps such as Pages, GoodReader, DocsToGo, etcetera, but there are also quite a number of apps that use their own document format and/or do
not support synching. An app could even use a common file format such as PDF and
still not support synching. In that case GoodReader cannot exchange files with that app, even though it reads PDF files. That is due to the way the iPad file system works. The iPad does not have a general file system that is available to all apps. If the app uses its own folder for storing files, GoodReader (or any other compatible app) can't see it at all.
Let me give you one example: WebOffline is an app you can use to store an entire website locally on your iPad, so you can view it even without an internet connection. A website consists of text (html) files and images (jpeg). Both can be read by GoodReader, but GoodReader simply does not know anything about any stored website in WebOffline. For the same reason, GoodReader also can't send any file to WebOffline.
That means you can not -at least not completely- sync two iPads this way.