It is going to depend on what kind of video and where you are getting it from. If it is just a movie, say mp4, then it should work no matter which it is on. At least as long at the video app you are using will read from the card. You would need to make sure its settings allow that.
Now if you are say downloading from Netflix, which I know is a new feature they have, then it won't work on your SD card, or if you try to move it to anywhere else. They have restricted the ability to move them and run elsewhere. For obvious reasons.