No - in this time period only COSC versions of Omega's 7750 based calibers received serial number on the movements, so this one will not have a serial number for the movement.
I just went back through the photos of the last 20 or so of these 7750 based Speedmasters that I've serviced, and none of them have the serial number printed inside the case back. I don't service the reduced models (modular chronograph models) so I don't have a lot of experience with them, but I don't believe your theory applies with the various Speedmaster Date models.
It's up to you, but with the serial number removed, and none present on the movement, Omega may refuse to service this watch in the future. Personally, for that sort of money I would send it back.
Click to expand...