Catchment isn't an issue, there are 1 million passengers within CWL's long haul catchment. People will come down from BHX if the price is right, same goes from the far south-west and along the M4 too.
If the UK didn't have an abysmal and inadequate motorway network I'd be inclined to agree with you, but we don't and frankly, as a Midlander, if I couldn't get out of BHX at the right time / right price my second choice would be MAN, third LHR. Frankly a trudge down the M5 / M4 or M5 / M50 / A40 / M4 then across country to Rhoose wouldn't figure in my plans, however cheap the prices.
Hopefully there'll be enough traffic from South Wales and the English side of the Severn crossings to sustain Qatar, and if it has the range, a smaller narrow bodied aircraft would seem a good way to start the route.