I don't have much of a frame of reference, but I do think it can help add to an understanding of Aikido...and I do feel fortunate: it's a very rare mix, even more so outside of Japan. It's definately an interesting and beautiful place and I appreciate the atmosphere for helping to instill a certain mindset. I'm a big believer in the impact our surroundings have on our state of mind and I really like the idea of cultivating sacred space for potentially adding to "deeper" interactions/operations. For example, I find the awareness of the centerline running through the jinja has a direct impact on how I pay attention to the centerline running through my own body.
Also, the fact that sanpaisha will occassionally ring the bell and pray at the entrance during keiko, which demands we completely avoid the centerline, adds to the demands for awareness and consideration of our surroundings in general.
...Of course that can be found where ever we put it, not just in a jinja, but that's what I find to be reinforced in what little I understand of Shinto and Aikido.
I really like the example that you give here.
I am not familiar with a prayer during practice - but I can imagine that it will highten everyones level of awareness.
It really sounds like a special dojo - will have a look at the website (it does have a website?).