the first day when i learned tenkan, it seemed to include a pretty obvious philosophical implication. "ok now we're looking ACROSS each other, (tenkan), and now we're looking in the same direction. SEE?"
I would certainly count this explanation of tenkan as 'hooking into the spiritual side of Aikido.' I would say that teachers who use this sort of language regularly are conveying a spiritual message. Does anyone have teachers who regularly go beyond this and talk directly about "the great spirit energy" and the importance of studying Aikido because it "brings the whole world into harmony"? I've never run into this personally, although I would claim that most of my teachers (especially before I got to ASU) made a point of emphasizing the spiritual side of Aikido.