Alfraz,
So what your saying is that integrated students have a ever slightley better chance of employment and that ever so slight advantage really matters when getting your foot in the door for the first time?.
What I think is that 'big school' (well know, established, well networked with the major recruiters, etc) training will give you a better chance of getting your foot in door. I say again that 'big school' does not necessarily mean integrated.
Don't get fixated on the word "integrated". I suggest you do some research and find out who the big players are in the training industry, you will fine one, maybe more modular providers in there.
One errant thought that has struck me about schemes like OAA APP, is what if you are not put forward for interview by the school during a time of strong hiring. Could that raise questions in the mind of a recruiter?