Senior people of my school, and especially the school on Maui, do a lot of meditation, both in the dojo and privately. They say, if you are serious about Shin Shin Toitsu you will probably end up doing this too.
At the moment I have to take this on faith. I can see arguments why there might be a connection, but I can't actually perceive any in my own practice.
If nothing else, ki breathing has inarguably been good for my lung capacity and ability to sit seiza.
My dojo does ki breathing, or occasionally the expansion/contraction meditation, at the end of every second or third class. I don't think we do it long enough to accomplish much other than teaching the technique, though. It's up to the students to take it further if they want.
If I lived on Maui I would do the meditation sessions at the dojo there. I don't know what it accomplishes yet (intellectual answers but nothing from my own experience) but I feel like it has something to offer.