Will this lens and teleconverter work OK together?

I have the Nikkor 70-200mm f/2.8G ED-IF AF-S VR Lens. I'm looking to get double the length on it for sports by adding a 2x teleconverter. The loss of 2 f-stops is not really a problem, as i shoot mainly in pretty bright light. Would this lens work ok with the Nikon AF-S TC-20E II Teleconverter? I know it is the older model, but I was looking to not spend a huge amount as I can't really shell out $600 for the AF-S Teleconverter TC-20E III right now. Will this teleconverter work well with this lens? Thanks

Added (1). No, i know that they will work together, i just meant like would it be a good match up quality wise and how well it would work

Did you go out to the Nikon website to see what lenses the Nikon AF-S TC-20E II Teleconverter.

There's a list of the compatible lenses there.

Should do just fine