lets take a look at the first part. it's not as simple as a touch. a number of things need to happen for the "connected". Ikeda sensei often asked uke to be "strong as you can", i.e. provide a stiff frame of your body, stiff force if you will. this would take the "slack" out of uke body which makes it easier for nage to work with (learning stage here). now if uke just goes limp noodle, then it makes it much harder, because there would be too much slack, i.e. gaps in the body for good force conduction.
the next part, nage has to take the slack out of his/her/it body as well. otherwise, we have the same issue as uke slackness. however, unlike uke, nage takes the slack out of his/her/its body through body conditioning to create a fully connected body without stiffness like uke.
a few more things to add. when you heard Ikeda sensei said "no space". it meant to remove all the slack within nage body and uke body, i.e. no gaps for better force conduction which is one of the requirement for the second portion of Unity. "no space" doesn't mean external physical space.
one thing that i had problem with the setup. Uke provided the stiff force, "strong as you can", which inevitably folks would tensed up all the muscle in their body. read about tetanus in this paper http://people.eku.edu/ritchisong/301notes3.htm
. once Uke has tensed up muscle for awhile, the muscle fibers had not the chance to relax. then Uke switch role with Nage to perform the exercise. the result is that the new Nage now too tensed to do the exercise. i usually felt my body tensed within an hour practicing stuffs. so for folks who attend seminar with Ikeda sensei, don't tense up when you are Uke. you can still provide a stable, stiff platform for nage to use (this is a learned thing), yet not tensing.