This is (kind of) the route that I'm taking. Having done lots of theatre- acting, directing, writing and producing- I'm more interested in moving pictures at the moment.
There are lots of ways in which it is good and helpful, but they are very different disciplines. I think that theatre is as useful to filmmaking as running a building site is. It will teach you leadership and how to bend people to your will, but really there aren't many similarities.
The acting in film and theatre (whilst, obviously, more similar than being a builder) is totally different, so learning one won't necessarily help the other.
The way I think about it is that they are like squash and tennis. Both raquet sports, both good for people with decent hand eye coordination- but, at the end of the day, they are sufficiently different that it's almost impossible to be really good at both, without bad habits from one or the other carrying over...