First of all, my understanding of aikido is that most of its great masters (including O Sensei and his teacher himself) learned technique first, then once they grasped the basics of the art, set about learning softness and ki.
I don't think that connection (kokyu) is synonymous with softness,or in fact related to it in any way. It is true that when you get most people in a physical contest (or what they think of as such), they're more likely to be too hard than too soft, but I don't think that the solution to being connected is to find the exact right spot on the hardness-softness axis. I guess it's a necessary but not sufficient condition: you can screw up your connection to your partner with too much hardness or too much softness, but to get connectedness, there are more elements that need to fall into place.
Connectedness is one of Chiba Sensei's five pillars. It's a fundamental, not an advanced topic, but you do have to experience it through technique and mechanics. When connection exists, that's how you get the sense of what you can do and when you should do it. When connection is lost, that's when the opportunity comes for a reversal. Unfortunately, the connection exercises in isolation make it very hard to see this.
The first time I got a glimmer of what this "connection" blather was all about was doing sitting kokyuho with my sensei. He kept saying, "Stay connected, stay connected," and I was thinking, "What does that even mean?" Then he did the technique and talked his way through it, while losing connection: "Now I've got it...now I just lost it." As soon as I started focusing on "what's happening now/what am I feeling", I could feel the difference. We practiced for probably half an hour straight like that. From that point, I could start to feel when connection went away during a technique or wasn't there. If "connection" is a big deal at your dojo, maybe you can get your sensei or one of your sempai to try something similar: a very simple technique where they deliberately lose connection at some point. It is a good practice -- awareness of connection, and the ability to maintain it, will really make your techniques much more effective.