You can ask all you want, but it鈥檚 absolutely no guarantee you will get what you ask for.
I send 2 Watches to Omega, with clear instructions. Twice they gave a shit and ruined the Watch for me.
I wouldn't recommend sending any watch that is worth something from a collectors standpoint.
A minute a week is still within the factory average daily rate of -1 to +11 seconds per day. If you send it to Omega it may come back 77 seconds a week fast 馃檨.