Yes, you still have access to the full disc, including Trailers, additional content, etc. The ability to bypass the trailers, warnings, etc. by selecting "Play Movie," is an option, it is not a requirement. Selecting "Play Disc" will cause the disc to playback just as it would in a BR/DVD Player.
That said, the contents you mentioned, in particular "extras," can only be accessed if they are available. As a few forum members have noted, some content downloaded from the K Store has been limited to the movie only, with the "extras" being noticeably absent. The physical disc version of the same movie, if imported, will of course display all of the content available on the disc.
Jim