Okay, here's my question.
Does the specialized breathing methdology itself "affect" the internal connection *or* does it simply allow for a sort of internal feedback that allows you to sense and therefore maintain the "internal connection"?
It "affects" the internal connection (i.e., conditions it), although of course it could be argued that there is also an unavoidable bit of feedback also. But you open a can of worms when you get into this discussion. You want to be careful that you're conditioning the right parts and not the muscular-tension parts (which is what far too many people do when they think they have discovered "breath training"). In other words there's a trick to getting hold of and conditioning the right things. Although Tohei and Ueshiba were careful to delineate this problem by insisting on very relaxed breathing practices, my personal opinion is that they would have helped a lot more people if they'd been further explicit than just saying "relax". That's pretty reminiscent of all the people who wound up doing bogus Taiji because their Chinese teachers just kept saying "relax", but didn't tell them any of the other important details.
If you want to draw power from the 'relaxed' breath training, there still has to be some way of generating power and that comes down to using the hara for controls and to having the whole-body connection getting stronger through proper exercises and the concurrent use of "kokyu" throughout the body. Kokyu, hara, ki/breath/suit, all together is not really a difficult idea to conceptually grasp, but to implement it is pretty hard because it means changing the way the body moves and breathes. Well, of course I referring to the traditional system that Ueshiba seemed to subscribe to, not other approaches.