In general, monitor arms should not damage the desk, but there is some risk of that happening depending on the type of monitor arm you are using and how long you keep it on your desk. If you clamp the monitor arms to the desk, there is a chance the desk surface will get scratched. Luckily, many monitor arms have some padding on the underside of the clamp to prevent this. You can put a piece of thin fabric down first to prevent scratching if your monitor arm does not have any protective surface.  If you leave the monitor arm clamped on your desk for years and years, you will likely have some difference in color between where the clamp has been and the rest of the desk.