I experienced it all
Sometimes bag came out first with the priority tag, even if I flew in Y and checked in early.
But usually it doesn't - there isn't any consistency with BA on that matter.

Usually the rule of thumb is; on container planes - the later you check in, the later the bag will be loaded in the last container the earlier it will be on the belt at your destination.
But this also does not always apply - at any airline tbh.

I usually travel with a checked in bag (although I completely respect the quality of life traveling only with a cabin-bag) and if I look back on the last 12 months; I have traveled on 6 different airlines (with the majority being BA) and the only one where (out of 8 bag collections) my bag was consistently amongst the first was with SAS.
All other flights with the other 5 airlines my bag came out at random despite a priority tag.

Now what really could be improved is airports enforcing the rule of standing 2 meters away from the baggage belt instead of having your knees touch the belt (which are mostly middle aged men with Bronze status - don't shoot me!) - that would actually help a lot more than any red or yellow x-mas decoration on your baggage tag.
I should really get a petition going