If you want to do sound to accompany video, then it would be very helpful. If you want to do sound for music, then not so much. Video requires knowledge of sound because it always has a sound component that you need to be able to work with. Sound doesn't always have a visual component, but when it does, the same level of coordination is needed.
The technical skills of a video editor, a cinematographer and an audio technician are all very different. The language used and even the workflows are very dissimilar. That said, there are some aspects that are useful across disciplines, such as general understanding of signals and processing.
There are also two main schools of thought, you have the Hollywood breed who specialize in their art and their art alone, depending on others to fill the other roles. You then have the independent film makers who have to know a little bit of everything, but don't necessarily master any of it.
I'm personally in the latter category and while I can do my choice of audio, video or lighting at a professional level, the amount of cross benefit is not substantial. My advice would be that unless you have a need to work with video guys or have an interest in it for yourself, you probably don't need to bother.
If you do want to learn, I recommend starting out just playing around with some basic footage and trying to tell a story with it. Once you start getting some of the basics, hop over to Video Production and read some of the beginner questions or ask your own. If you have any contacts with any local film makers, perhaps volunteer your audio services in exchange for them showing you some of their side of the art.