Can you remove the serial numbers from your own stuff? Yes.
Is it a great idea? No.
First - should you ever want to resell it, there's a Penal Code section (PC 537e) that makes it illegal to sell items with serial numbers removed.
Second - should there ever be a question of whether or not you lawfully possess this item tracking it through serial number is the easiest way. If there are allegations that you stole it (or that it was stolen and you now possess stolen property), missing serial numbers are going to hurt you - in a big way.
I'd seriously question your motives (or your friend's) in the idea to remove serial numbers.
Why would you. This is a common practice upon those that steal items. The numbers are there for your protection in case the item is lost or stolen so that you can recover it. Should the police ever suspect that the items are stolen this would not look good for your friend.