Do I need to drill into my desk to install a cable management tray?

No. The majority of popular trays use either a clamp mount (which grips the desk edge with thumbscrews) or strong 3M-style adhesive. Clamp mounts are generally preferred for heavier loads like power bricks, while adhesive J-channels work for lighter cable runs and rental-friendly installs. Most candidates here offer screw mounting as an optional upgrade for permanent setups.