Howdy Chris,
I would love to help you with this.
You can certainly import from multiple Facebook organizations. However, you would have to manually assign a category to the imported events if you wanted them to have one. Facebook events will not have categories by default. To make this easier you might could set automatically imported events to drafts, That way before they appear on your site you will need to to hit the publish button. Before hitting publish you bulk edit the events to add categories, then publish them.
Does that all make sense? Does that sound like it will work for you? Please let me know.
Cheers!
– Brook