From VIII:
STATEMENT OF POLICY ON THE USE OF ASME MARKING TO IDENTIFY MANUFACTURED ITEMS
The ASME Boiler and Pressure Vessel Code provides rules for the construction of boilers, pressure vessels, and nuclear
components. This includes requirements for materials, design, fabrication, examination, inspection, and stamping. Items
constructed in accordance with all of the applicable rules of the Code are identified with the official Certification Mark
described in the governing Section of the Code.
Markings such as “ASME,” “ASME Standard,” or any other marking including “ASME” or the Certification Mark shall not
be used on any item that is not constructed in accordance with all of the applicable requirements of the Code.
It can be done, as Al states with 'work arounds', i.e., a reconciliation. I've done a few of them. Its always difficult and most often impossible. The operative is that you must be able to demonstrate that the fabrication was performed in compliance with ASME. This does not mean that it was intended to comply ahead of time. But if not ahead of time it becomes very very difficult.