Jordan,
You'll never have a problem (I know, never say never) with a Bren barrel in your carrier for display, etc....but since you'll never be using it "for real" there is no harm in welding a steel rod into the barrel and plugging the gas port, just to be on the safe/legal side.
Technically, owning ANY part to a prohibited firearm could be grounds for breaking the firearms rules...now, would anyone call you on it? Probably not, but as has been said, better safe than sorry. You know as well as I do there are always people looking for things at our kinds of events
Tim