When Shaco, Nocturne and Fiddlesticks get their eventual reworks the demons should get more lore to flesh them out. I think it'd be cool for them to be classed as their race and get a faction icon. Right now they're just listed under Runeterra. No idea what the icon could be but I'm sure Riot could come up with something cool.
I like the idea, but I don't think you can classify demons like this.
The Darkin have similarities - they're a unique "species", so to say - but demons are just malevolent spirits. Each demon is distinct and independent, shaped by humanity differently than other demons; there's nothing unifying them into a single faction, and while the Darkin would most likely work together, demons would fight over their territory.
That said, Riot could create two different icons related to spirits: one for positive or neutral spirits like Bard, Janna and Kindred, and one for negative ones like Tahm Kench, Nocturne and Evelynn.
I don't think there is anything that really unifies all of them that would work.
I think the next time they release a demon(or maybe a spirit in general,as demons are a kind of spirit),they might do this. Because currently they always give us a lore update with every big release(we got ones for Noxus,Kai'sa,Irelia,Pyke and will certainly get one for the darkin),so I guess that the next time we get a demon or spirit we'd get an update for their race as well.
However keep in mind that at least based on the current lores only Nocturne would qualify as a demon.
Shaco is described in his new lore as a living marionette and Fiddlesticks is essentially an undead(granted he is a ghost posessing a scarecrow and ghosts are kind of spirits themselves).
And the only confirmed demons so far are 
and 
