Sure, in theory. This kind of invalidates my joke, but Twilight holds no apparent power of state, and I'm pretty sure Luna is happy just to get control of her little barren, rocky satellite back. Celestia seems pretty well in charge of everything.
Then again, I feel like pony politics depends more on headcanon than most other aspects of the show.
Well, I imagine that Celestia abdicates whatever power she decides to abdicate. I doubt there's a formal structure in place for the other Princesses to help or give them any innate authority because of their title. She's always been the sovereign, so why would they have any such system?
I suppose it helps that the sovereign is an immortal being responsible for one of the most vital ecological functions on the planet.
If we had a ruler who was demonstrably a God(dess), I'd probably be a lot less into democracy too.