It seems unlikely to me. That number was assigned between April 1 and July 10 of 1914, and I think Wolf was still working for other pipe manufacturers at that time. I gather the stamping on your pipe is faint and difficult to read. Does the OP (or anyone else reading this) have a Wolf Bros pipe with a legible design registration number on it?
If it’s definitely 638866 I can start the wheels turning to order copies of what survived but would prefer a little more certainty first.
I have one I bought on eBay last year as a Town Hall. I bought it because I was looking for a silver Army mount to fit a gap in a cased set. Stamps were faint but after the MicroMesh treatment I could read Wolf and see the triangle beneath. It's a well used Condor pipe but the hallmarks are readable as 1923. It did not fit the case. Second pic is before I cleaned it up.