Dry firing as a function check will not damage your SiG. Repeated dry firing without a Snap Cap or similar in the chamber for more than just function checks can cause damage that can lead to a breech block retaining pin failure or damage to the firing pin. I refer you to pictures I grabbed form a related thread on another forum. These are NOT my pictures, but clearly illustrate the potential for damage when dry firing excessively.
Regardless of what the manual or a Customer Service Rep may say about it being safe to do so, I do NOT recommend doing so without the cheap insurance of Snap Caps or similar in the chamber.