A follow up on this for those that are interested. Monday at T5 I went through the same process of checking in for my Y flight at the business class check in. I asked for the priority tag as I’m BAEC Gold and was told “Sure, I’ll put it on, but it won’t make any difference”. It was further explained that the bar code on the tag indicates what class you are in, and these are loaded together in the larger bins, and premium cabins’ bins are offloaded first. This corresponds with the last explanation in my original post. I still asked to have the priority tag attached, which she did, with a smile.
On arrival, my bag was one of the first on the belt.
What to do in the future? Ask for the priority tag but don’t expect priority treatment. If the bag comes out first, consider yourself lucky.