It absolutely depends upon the application. My editor does. Typically spreadsheets do.

As a rule of thumb, if the application is modifying the file in-place, then it will deny read access, as any asynchronous read might read a non-coherant intermediate state.

That said, I've got three different video player apps, and even on the same filetype one denies all access, one denies write access and the third doesn't appear to care what other apps do to the file after it has opened it.