Airlines are looking for good quality training and I've never heard of them auditing training records (however, this could be different in regard to integrated/sponsored cadets but its obvious that we are talking modular pilots here). The FTO's you have mentioned have good reputations (at least as far as I'm aware) so I don't foresee any issues there.
You will probably be asked where you did some parts of your training but its just a general question, aviation is a pretty small world and it's likely that the interviewer may know someone that was involved at some point with your training or skills tests etc. Also, most pilots (myself included) asked instructors/HoT/CP to provide a reference on a C.V.
So to answer your question...No it doesn't matter. However, I would recommend getting some good CPL/ME training as it will make the the IR rating much easier to manage and save you money in the long run.
Best of luck
MP
