Is there a way to check whether an app explicitly supports Resume or not?
Most "Lion-Ready" apps will also support the new full-screen mode, so if you see the little full screen button, it is likely the application will also support Resume. However, there is no definitive list that I am aware of yet, nor is there a way (beyond a mention in the app's documentation) of knowing whether it will support Resume.

However, there is now a list of "Enhanced for Lion" apps on the appstore which might be a good place to start.