DIAGNOSIS: You can, but you have to be smart about placement. The risk isn't the weight, it's the concentrated clamping force and potential for the wood veneer to chip.
FIX: The key is to clamp the arm onto a structural part of the desk, not just the thin desktop material. 1) Locate the metal frame underneath. Your arm's clamp should be positioned so it's gripping directly over one of the side rails of the frame. 2) Use the included rubber or plastic pads in the clamp to prevent scratches and distribute pressure. 3) Tighten the clamp just enough to hold firmly—don't crank it down with all your might.
IF THAT DIDN'T WORK: If you're nervous or have a very heavy setup, use a grommet mount instead of a clamp. Drill a clean hole (check the arm's required size) through the desktop in an unused area. The grommet mount distributes the weight vertically through the hole, eliminating clamping pressure. Vari desktops are designed to support a grommet.
HEADS UP: Never clamp a monitor arm on the very back edge of the desk where there's no frame underneath—that's a sure way to crack or dent the top. Also, avoid mounting it on a desktop made of the thinner "reclaimed wood" option if you have a super-heavy monitor.