From experience ..

.. in the retail industry most UK companies don't bother taking a note of the serial numbers when they hand the stock over to customers anyway.

So yes, the manufacturer may be able to tell the police which wholsaler had the machine, and they can probably say which chain/branch they delivered it to. However the retailer is likely to say "sorry, we don't keep a note of serial numbers".

This may be different in the US but none of the retailers I've worked for bother.