Some airlines have relationships with some schools, which can enable suitable CVs to go straight to the top of the pile. Such a relationship can be an advantage, but just because you train with x doesn't mean you'll walk into a job with y.
Right now it's a pretty academic point, as no-one is recruiting in any significant numbers, and the situation will almost certainly get worse - probably much worse. I would strongly recommend delaying CPL/IR training for at least 2, preferably 3 years. You have 36 months from passing the last ATPL exam to get the IR, so the timing works.
Qualifying in the middle of a recession is a very bad idea.