I'll start by answering my own question so as to better define it. We learned from Lea in Ghost Story that Mort Lindquist hid his true ability from the Council. Lea said that Mortimer's power level was likely greater than Harry's, though limited to his own field of expertise. Elaine deliberately hide her abilities from Warden Ramirez. Harry knows Cowl is White Council material, he even speculates that Cowl and Kumori hide their identities because they are Council members, but Harry could be wrong. At least one or maybe both Necromancers hide their identities of the more obvious reason that they simply don't want to be recognized at any place or time. Even Necromancers have to go to the supermarket after all. They can't really send a ghost and sending a zombie would require too much effort and defeat the purpose of being incognito.
I wonder if there are a significant number of wizards who are hiding their true abilities. Some of them might be like Cowl and Kumori who chose a dark path and need to hide from the Council, while others might have met a warden when they were younger; say someone like Morgan explaining what happens to a person who breaks the laws of magic, and decided, "These White Council guys are as**oles, I don't want to be any part of their organization."
I find it hard to believe Elaine is alone in her feelings about the White Council. I wouldn't be surprised if not everyone Harry dismisses as the "have nots of magic", the people who hang out at Mac's, are really below White Council standards.
There almost certainly are some other Council-level 'wizards' who hide their power and ability from the Council, but there aren't likely to be very many.
Why? For one thing, Council-level
potential is rare. There aren't very many people in the world who have even the
potential to reach that level to begin with. Of them, the majority probably never get trained to the point where it matters, or else end up blowing themselves up or getting beheaded experimenting on their own.
To become a Council-level talent requires both that raw potential, and training to use it, and it's hard to find the kind of training that will bring you up to Council-level except from Council-level adepts.
Harry and Elaine, for example, if they had been adopted out to normal people and not Justin DuMorne, would likely never have come anywhere close to realizing their potential power. They might or might not have learned to use some magic, but without high-level training they'd probably have remained minor players or worse..
DuMorne, of course, was a rogue Council member.
It's going to be a rare, rare person who can reach Council-level without the proper training, and it's going to be rare for anybody not linked to the Council to be able to provide it.
There are several thousand Council members, IIRC. That sounds like a lot, but that's out of closing in on 8
billion people. I doubt if there are more than, at the most, say a 100 people in the world with Council-level talent and training who are not part of it.