major wannabee - The CAA website does not list Airmed because the CAA does not approve it, that is done by the Spanish Authority. Similarly, the CAA website does not list FTOs approved by the French, Dutch, German, Swedish or any other JAA member state's Authority.
As to the acceptability of licences - In theory a licence issued by any JAA member state must be accepted, without formality, by every other JAA member state. However, as the French DGAC has shown, this does not always happen. In most cases a JAA licence issued by Spain will be as acceptable throughout the JAA as the same licence issued by the UK, in some cases more so. Tino, the representative of the Airmed marketing department, is quite right in saying that the licence obtained after an Airmed course is the same as that obtained after, for example, an Oxford or Cabair course. That is not to say, however, that the quality of training is the same and the airline training departments are well aware of which FTOs turn out the most employable product.
The hard fact is that, in the present climate, you will have little chance of getting into the RHS of an airliner no matter where you train. When things begin to improve (and your guess is as good as anyone else's on that matter) graduates from established schools with good reputations will, as always, have a slight advantage although the proclaimed benefit of an 'Oxford education' is vastly overstated. There are a number of airlines that are becoming increasingly disenchanted with the concept of 'integrated' training now that the constraints of the JAA syllabus has resulted in students being trained only to pass the exams. I know of two UK airlines that have a policy of rejecting any and every application from integrated course students.