This seems like a widespread view, but what I don't understand about it is that there are similarly extensive footballing pyramids in the other countries that do use the B system. It's not like all of them just have a few tiers and that's it.
Of course it played a role. The concept of it is that you're playing competitive games in the system that you're going to utilize when you step up to the "A" team. If you get loaned out, you might play.. but there's no guarantee of that and there's also a high likelihood that you won't play in the same style as your own home club. The B team players also can still train with the main squad, can still play in the Champions League (Julian Green got a few minutes in it) or other cup competitions, etc.
Yes, they had a shitty World Cup, but look at Spain's squad. Almost all of their players have multiple seasons for their respective clubs' B teams.