Diagnosis
You can, but you have to be careful about placement. The bamboo is strong, but a clamp exerts a lot of pressure on a small area.
How to Fix It
Always clamp the arm directly over one of the internal steel frame rails that run underneath the desktop. These rails are the structural support. You can feel for them by tapping—they're solid, not hollow. Position the clamp's jaws so they're centered on the rail. Don't overtighten the clamp more than necessary to hold the arm steady.
If That Didn't Work
If your monitor arm has a particularly aggressive clamp or you have a very heavy setup, consider using a reinforcement plate. It's a small piece of wood or metal you place between the clamp and the desktop to distribute the pressure. You can buy these or sometimes they come with the arm.
Heads Up
Never, ever clamp directly onto the unsupported bamboo surface between the frame rails, especially near the edge or a cable grommet hole. That's a surefire way to dent or crack the bamboo over time.