You seem to be missing the point. There is no faith required to believe in Arceus. Arceus is readily observable. He has even been known to tell us what he wants. Religion is faith based. Hence, the study of Arceus, what he does, and praise he recieves is probably not going to resemble a religion in any way.
It would be like if the people of Metropolis started worshiping Superman. No faith required. Say hi to him and invite him for a coffee next time you see him.
Or if we started worshiping a celebrity. It's just not the same when the thing you're worshiping is readily observable.
With Arceus, there is a really strong basis for someone to start a religion. The people who have abused their gift that Arceus has given them have ignited its wrath, thus it took away the gift of Pokémon. But after around a century or so has passed, it gave humanity a shred of remorse, & gave us back the gift of Pokémon, albeit in a different form.
Still people take this gift for granted, so the way I'm going with this is that people should be grateful for Arceus for forgiving us for abusing its gift in the past, & should try their hardest to regain Arceus' favor.
I don't think religion works anything like it does in the real world here. Reason being: People don't really need to rely on faith nearly as much. God's name is Arceus and it ripped open the very earth and gave us pokespirits in front of our eyes. If you go into the streets and denounce Arceus, absolutely nobody will take you seriously.
That being said, a cult as you define it seems rather unlikely. The underground might have the closest thing for Lizzy Borkson.