Nikon Z6II

Without the paid upgrade to record BlackMagicRaw to the Video Assist 3G from the Nikon Z6II, would the camera and monitor be compatible at all?

I want to get both the Nikon Z6ii and the BlackMagic Design Video Assist 7" 3G Recording Monitor but would be some time before I can pay for the firmware upgrade to be able to record using the new codecs.

Yes, you can still use the Nikon Z6 withnthe new VA 3G, you will be able to record ProRes files in both 8-bit and 10-bit output mode from the Z6 and new Z6II. You can later do the hardware upgrade to the Z6/Z6II to get BRaw recording capability.
Cheers