If we install and activate the Q4 2020 tax table and we process a payroll with a December check date, will it calculate the taxes based on the 2020 or 2021 tax table?

It will use the 2021 tax tables.  Best time to install & activate the Q4 2020 tax table is after your last December payroll is completed and before your first payroll in January. 

It will use the 2021 tax tables.  Best time to install & activate the Q4 2020 tax table is after your last December payroll is completed and before your first payroll in January. 

We are using Sage Online, they have the notice up for the Mtce to be completed on December 19, 2020, which I would think will include this update for the Canadian Payroll Tax.  Will I still be able to run one more payroll using the tax tables for 2020 after they complete this payroll tax update? If I'm not mistaken, as long as I don't complete the "Data Activation" under the Admin Services I hopefully will still have access to the 2020 tax tables? Once done, then I can run the Data Activation to get the 2021 Cdn Tax Tables?

you will be fine if you don;t activate the 2021 tax update.  Just run it before you run your 1st payroll of 2021.