Frankmatt
just following on from what propellerhead said. BA won't give two figs about your qualifications or phd course. it's about whether you would fit into their company ethos, team work skills, commercial awareness etc. so no they don't go on qualifications or being over-qualified, it's impossible in this business.
and your other question about degrees and post-grad degrees, no is the short answer. a few friends of mine fly for ryanair, none have degrees, one doesn't even have any a-levels, it matters not. all about skills, coolness under pressure...list goes on.