AL historically have never recruited direct from the flying schools.
Actually they have and I have been around long enough to see it. It is easier to ask a respected FTO with whom you placed cadets previously to recommend a few of the better individuals and avoid having to wade through reams of CVs from hopeful wannabees. But you are correct there is no network as such. The individuals concerned had no link to AL. But it never does any harm to have a good reference from within or from certain FTOs. But Aer Lingus is not unique in that.
There are also known for favouring integrated over modular when hiring recent graduates. They are of course entitled to do so. That's just a heads up for applicants. Doesn't apply to experienced type rated pilots.