Done this several times, in Auckland, Bangkok, Tokyo, and although the check-in agent usually had to speak to their supervisor, it was absolutely no issue to check-through.

They do usually check the class of your onward travel and hence luggage allowance and make sure your bags are within the weight limit for your onward ticket, so if your onward BA (or other OW ticket) is in economy, don't assume that you can get away with QR shovelling business class baggage all the way through onto BA. I remember in Auckland that I exceeded the standard BA economy allowance but was within the limits due to my BA status at the time. I would imagine trying to check through onto a BA economy hand baggage only which has no luggage allowance might end in tears.