2sheds:
it does presuppose that the aircraft is receiving service from a radar-equipped unit and is identified
The former, yes, but not necessarily the latter. I see no reason why the current formulation 'G-CD traffic believed to be you has traffic in your 12 o'clock one mile opposite direction no height information' should not continue to apply under a BS. And just as with FIS, it's contingent on the controller having the capacity to give that info.
NS