I use LDR as a way to bring the horse's attention back to me, to assess soundness and the physical being of the horse, as a stretch in my practice of in-hand and under-saddle flexion, and to help with bringing together different points in my training. The position is acheived with softness, for short periods of time. My horses are asked, and if they put up a fight or give me tension, either I'm doing something wrong or they are hurting/not ready to stretch in the way that I'm asking (so, if I'm asking for a stretch under saddle at the walk, but my horse isn't understanding, etcetera, I'll go back to the beginning and try it in-hand and see if they understand.)
But, I don't think of it as teaching "connection" in the sense of the hind end connection, because the postion still tightens the lumbar spine (but doesn't lock it completely, as with hyperflexed horses), making it impossible for the horse to move completely underneath themself. In a sense, though, it can be used to "connect the dots" of some points in the training, whether we ask for it directly, or indirectly (for example, I'm teaching Freddy the meaning of how to stretch into the contact. Right now, he understands how to go forward and down, but he's still too unsure about stretching outward. So he appears to be in LDR position when I ask for "forward-down-out", and it will just take time for him to realize that I'm asking him to stretch into the contact, and that it's okay).
I hope that made sense.