Yes you can it is removable. However that second image you have isn't the right compartment.
That compartment is for the rear compartment at the back of the glovebox accessible by the passenger seats and the front one under then headunit. They aren't that cheap to honest and do break fairly easily If you are a little bit rough with them. The one you want is the compartment Calais have stock, which is a similar click to open compartment.
To remove the centre console use a trim removal tool or a screwdriver in a rag and begin to pry off the plastic surrounding. There are 6 clips located at the same position each side. One right up against the glove box, one in the middle of the centre console and one right at the end closest to the headunit. There is also a screw located underneath the front compartment located below the headunit. Once they are all I clipped carefully remove it be sure to remove the cables going to the window switches etc. If you search it in the forums there are detailed picture guides so you don't ruin your trim! Hope that helped
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