The FACT of the matter is that it is standard practice for airlines on occassion to call the largest FTO's and ask for a shortlist of suitable candidates from their self sponsored pupils.
I have seen this happen at BAE, OATS and CABAIR over the years. Because these schools do integrated courses and have relationships with airlines. They also are well known enough to be known by Chief Pilots and the like.
It is always done because of some unforseen event. Often unexpected expansion or loss of flight crew for some reason.
It is statistically a rare event. If I had to stick a number on it I would say perhaps 2% of self sponsored student on integrated courses get jobs as a result of airlines seeking graduates direct from the large schools.
In the good times a year ago there was almost a standing arrangement at BAE that the best one or two from a self sponsored course got a "recommendation" from the head of training. This went to BA who would then take you to interview stage and accept you as a direct entry TEP (if you will).
Believe me. Every course has its Atomic Chan ( as he was called in Jerez in my time ) who just aces all his flight tests and walks through the exams wondering what all the fuss is about.
You - yes you - are just an ordinary student who will become an ordinary pilot.
You should not plan or aspire to getting your first job on the back of a FTO recommendation. IT WON'T HAPPEN for you. Its akin to getting airborne with not enough fuel and hoping you get a tailwind...
I have never seen an advert requiring applicants to have graduate from a certain school. Sometimes an airline will specify that they want graduates from Integrated courses. Other times they want a minmum number of hours on a still frozen ATPL and don't care how you trained.
To be honest "the airlines" don't know jack about flight training and schools.
This shows by the naive way they ask for "the best" handful of students at times.
Looking just at exam marks and first time passes in flight tests is a rubbish way of finding the best line pilot. If they would just get off their backside and get into the instructors crew room and lock the management in the broom cupboard for 5 minutes they would do far better.
It never ceases to frustrate FI's that employers never speak to them about ex-students they are considering. I have seen the star of the course all round good guy totally overlooked because he failed Instruments first time or mis-identified village A for village B on their CPL skilltest.
I would recommend though that you adopt an attitude with your FTO along the lines that you WANT them to recommend you to an airline. You never know...
Good luck,
WWW