Will I really lose access to my account if I don't verify by January?

Yes, that's why you have to comply to KYC to verify your account so do it before the deadline.
I refuse to upload my documents because I was told I would never have to do so. I guess they lied to me when I signed up.
That's from before and I think most of the casinos have said the same thing. But all of them are subject to changes in compliance of the law and jurisdiction where they are at.
And as users, we have the option not to comply at all and if you've got funds there then you better withdraw them,
now!