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.
If you don't wants to upload your documents, you can search for other casinos that allow you not to do KYC. But I guess many casinos now will ask their members to do KYC.
They can changes their rules anytime they want so we as a gambler should understand that. You are free to do KYC or not because that choice will be up to you.
Many other casinos you can use to playing gambling but those casinos will ask the same thing to their members.