I think although BHX/LHR are close to BRS there would still be a demand for a ME departure from BRS....If you look at the current operations in the UK, EK operate from GLA now twice daily and from NCL, which is about (?) to be upgraded to a 777 from an A330. The distance from EDI to NCL and in fact GLA from EDI cant be too different from where BRS sits in relation to BHX/LHR etc... But we know that the Bristol catchment area covers a fairly large area. After all not all the pax on the EK flights from the other airports are purely from within a 50 mile radius! The people of the SW have to travel from somewhere!
If QR feel that EDI would work with competition from a rival not too far away, I can't see why this could not be the same for a BRS departure.
I am basing this purely of my own experience of trying to fill these seats for the airlines and whilst there may not be a massive demand purely for the ME, there is big demand for eastern connections that I think might make a QR flight work, even with just 2 AUS points of arrival at present.