I don't think she's a member of the Jade Court. As noted by @segaily, that would mean passing undetected by the entire Senior Council. Fooling the Merlin, fooling the Blackstaff, fooling the Gatekeeper, fooling Native American Joe... I really, REALLY don't see all that!
On the other hand, let's look at Harry: co-habited with a WCV for a couple of years, regularly allies with him on missions, is blood related... If the White Council knew all that, they'd go batshit crazy.
So Ancient Mai could well have some deep ties into the Jade Court, and them to her, that the Council wouldn't be OK with and that she must keep secret, just as Harry has to.
I expect ALL the Senior Council has secrets... both secret strengths and assets, and secret flaws and vulnerabilities. And what we know about the Dresdenverse's Far East... well, it could be nicely summarized in about 1 page. PLENTY of space for Mai to have secrets!