No. Not without building upon it. While the version of the FB PHP SDK (3.2.3) that the module relies on supports uploading video, there is no support for it in the module.
Looking at the current module, it looks possible to build in support. For example, take the scenario where the module supports uploading an image to the user timeline:
Presumably, one could extend another class (e.g.
FBAutoPostEntity that would add the various details for base classes that would allow it to plug in to the underlying SDK.
To sum it up, the existing module doesn't support however there's some support at lower levels in the code. That comes with the caveat that there might be more overhead to add (e.g. is there more to defining a Video entity than just extending the
FBAutoPostEntity class) than what I mentioned here.