[@Altered Tundra]
Yes and no. 'Traditional' Guardians, who live a life devoted to spirits and mediation, are obviously religious in that sense. But, Guardians created from spirit migrations, such as in this story, don't have to be religious in any way. Spirits choose their hosts based on other factors during times of duress.

There's a line about this in the codex, although short: "A spirit cannot use the languages of human beings, but they can show emotion through action and sound." It's the only thing I wrote on the matter. But, as you ask, there wouldn't be any kind of telepathic connection. Spirits can exit a Guardian's body and show emotion and wishes through actions and sound. These 'actions' could be pointing to things or drawing sings in the ground. Spirits do have their own, distinct personality and it is not affected when being absorbed or siphoned by a Guardian/Renegade.