Well, the exact relationship in the precursor Buddhism is probably something to look at. Take a look at the Kongourikishi statues (the A-Un gods, aka "Buddha's Warrior Attendants"). These are the Yin-Yang powers that appear to have originated in India, but were commonly seen in China and Japan, too:
"A" and "Un", like in "Aunkai".
The point is, how do you differentiate these obviously warlike statues of Buddhism into "secular" and "religious"? I doubt that the differentiation is all that clear, so for Ueshiba to use Chinkon Kishin training and say that he adopted "religious" practices is not a definition we could do easily. Well, it's pretty clear that these are body-training exercises and that's what Ueshiba used and so to teach "Aikido", that's what Tohei had to use.
Uh huh. Off hand, it seems like the preponderance of the evidence seems to point in that direction (at least as far as Chikon Kishin goes.)
BTW, your Sendai-biyori link brings back nice memories of that pretty city.