Well is this possible?
Time first based on both of the animes yes counting the secondary seasons as well it can actually work considering they are near in release dates but the timeline hmmm... blue exorcist is based on 2011 and Noragami is in a later date.
For the anime timeline, it works as well
Here's the biggest thing AGE Rin's age 16 and Yato's unknown as of now so the question is it considered as a crime to have to relationship or in world standards it's okay
Currently, we can safely consider Rin as a minor while on Yato's case it's 1000+ years if you count it then Rin is like YATO's child at this point
Appearance-wise Rin's age matches well with his character design and personality as well as someone said loud anime guys are the best!
While in Yato does maybe not or maybe yes we can't know with him at all but appearance-wise he does closely resemble an 18 years old man and his personality does have this moody feel on him more serious like than loud.
Rin's personality has this jump in first before thinking type I mean by the first episode he always gets into fights because of justifiable reasons. He likes helping but in his own ways supportiveness is natural to him and as the brief summary says he is loud and brash as well determinedness is his own motivation.
Yato's personality is a complicated one it's either by his mood or plain poker face all of the time but he's more of a feeler than a thinker means he has more empathy over others than other people have he so determined to get his dreams while he can come off as a self-focused person it's not his own fault either.
How does their first meeting look like?
Rin's supportiveness makes it easy for Yato and him to be friends almost instantly this happens because Yato does not have any ill intentions with any other people at all he's too kind for that to happen unless there are special cases.
YATO having a slight interest over to RIN because of his demonic heritage and rumors about him being a bloodthirsty demon that kind of relation between them being both an outcast always treated as a threat than a human being will make them have a strong bond with each other as well.
Relationship Wise who's more dominant and submissive?
(THINKING)
More on YATO's side for dominance because of his mysterious mood swings it's more natural for him to take an initiative as well and he can be the one that has possessive or protective nature for him as well you can take it either way.
For RIN I guess it's another natural thing but you can make a guess it's because of his age and personality but you counter as well that hey RIN can be dominant right!? Yeah, it's true but YATO has more initiative here for me.382Please respect copyright.PENANAM9GRvN63VU
YATO's straightforwardness works as well here you can never know if he's truly perverted or just protective.
The same goes for RIN you can say he has a more submissive nature in appearance-wise but you could also say that he can be the same as YATO more than ever.382Please respect copyright.PENANA9DzOTwiurY