Base 8,
This has been asked a few times in these forums, and the bottom line and the answer to your question is no.
As long as you have the necessary qualifications and licences that is all the airline will be interested in. It will you YOU that they will be interested in. The problem you face, and this will be no surprise, is finding the right path to securing that foot in the door.
There is no doubt that going to some of the bigger schools such as Oxford will effectively open more doors due to the fact they do have links with various airlines, however I know plenty of guys who have left these schools with no job and a little disappointed, as well as guys who have walked into a jet job with less than 200 hours. It is all swings and roundabouts and sometimes a case of being in the right place at the right time.
There are so many variables with this industry and it is difficult to give sound advice. But one thing I would say and back to the theme of the thread, is dont get stressed out about where you do your training.
All the best mate.