Definitely possible.  Currently playing a huge map, 10 factions - 6 of them randomly ended up being custom factions. 

Faction I specifically built for the AI - Trog, master scout, warrior, trained i think, lucky and vulnerable to magic, sov with armorer - is dominating the map.  I'm currently at the bottom of the power heap with 150 and he's at the top with 350 out of the 6 I've found.  Scary, but fun.

I did make a ruler for them, the problem is that under customize opponents, the one I made doesn't show up.  The ones added by Stormworld do, just not mine.

Yeah just make a sovereign with your faction....which you have to do to play it anyway....and that sovereign can be picked out the list of available players.

This actually does my God damn head in. I always want my opponents to only be from the stock list, but in order to keep my own creations out of it I have to customise my enemies, which then means I know exactly who else is on the map! And I'm not deleting my creations, it's a pain in the butt recreating them all the time.

Yea it's possible. In fact my AI controlled custom faction steamrolled me.