P.O.M.- FO Bloggs is quite right. As an ex-trashie, I can assure you there is no particular advantage during the recruitment process. It does give you some advantage doing the ATPL, as that is geared towards that type of aircraft operation, performance, systems, etc, etc. Trashies may also get a small advantage on the conversion due to having always flown a similar style of operations with performance consids etc, but it's all academic in the end.
Perceived bias for/against knucks, military and what-have-you is exactly that these days - perceived. The current pilot recruitment management are very even-handed, and recruitment of different 'flavours' of pilots pretty much matches the respective percentages of applicants. If you fail the interview its probably because you stuffed it up, not because you're a knuck!
Do the Len Sales ATPL course for miltary pilots if you can. Oh, and I second those remarks about bloody mirage pilots!
Edit: These comments apply only to QF at the moment. Can't speak for the rest I'm afraid.