Hi,
Yes OpenLP does support this. On the media manager (on the left) select the media tab. Select the video you want as your background and then click replace live background. Its the last button on the right above the media list.
However it isn't perfect. On our system, which is quite well spec'd (6 core Phenom, 8GB ram, Reason with 256/512 MB) the video plays a little slower than normal.
As also suggested, you could use a transparent theme and position a video player underneath. My favourite would have to be Screen Monkey (screenmonkey.org I think) if you had a system which could handle it!
VLC can currently be chosen as the default media player in OpenLP, however this is not currently used for background videos. I believe that this is planned, but it will not be until after version 2.0, as we have entered the Release Candidate phase of development (Bug fixes only)
God Bless,
Phill