I haven't tried to convert any movies - only my own recording from a video camera. I did try one, although I don't remember what it was, and was not able to copy it. My guess is no; it does not advertise anything about licensed video.
You hit on something I realized the first time I used the product. I am an instructor and purchased the product in order to put old VHS media onto DVD. All my original material was copyrighted and to date I have not experienced any problem. This got me to thinking that I could just as well go to a video store and start copying favorite movies. I'v not done anything like that but preliminary evidence suggests the device successfully captures all media, probably because its capturing the screen movement and not encoding directly.
I believe I tried a movie, but was not able to get a decent picture, so my guess is no. If the video tape is in some way encrypted, I doubt it will be able to copy a readable picture. There is nothing in the user manual to deal with this. I have only made copies of my old VHS tapes obtained by either recording old TV shows or on videocams.