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Quick Answer:
Yes.
But first you need to set a guide line for what you want the faction to be.
I think it'd be kinda intresting to see different users have Factions with Different OCs from other people

Ok sooo how would do that?

Um...
I dunno man I dunno how to start Either :/
so... a faction can be many things:
A country, an organization, a club, a species... the list goes on.
so first things first is identifying what the faction is made of.
Then maybe have try outs for the faction in the RP stream-
(or to save time you can do a google form and just collect the data there, if I make a faction thats how I'd do it.)
Then post a link to the Form in this stream.
Next maybe make a stream for the faction. for updates/jokes/mini Rps involving the faction.
Then, if you wanna get more attention for the faction: advertise it in your most resent/next Roleplay to all the people you are roleplaying with!

Thats how I'd start a OC faction. which thanks to your Idea I actually might!

So may start latter today.

yeah.
you don't have to follow what I say- thats just how I'd do it.
Feel free to make your faction however you want :3

Because I have no idea how to start it.