I don't think so. I know what you mean. Our Ford Focus had inserts that you could remove. Every once and awhile, they got removed and washed in warm soapy water, dry, then put back in. The ones on the Traverse look permanent.
I have removed the plastic liner from the cup holders and put them back. Take a knife blade (dull if you have one) and slip it just below the chrome lip where the flexible liner starts. This will flex the sides out from the lip so you can pull it away from the rim all the way around and pull it from the opening.
To remove the front cup holders, you have to remove the plastic trim from around the cup holders and gear shift. You may have to lift the bottom of the heat a/c controls and maybe the power outlet to get a grip on the front of the panel. Saw this while hard wiring my Valentine Radar detector yesterday. Finally got tired of the wire hanging down to the power outlet and the pigtail 2 plug job dangling in the passenger side foot well.