I think it is very probable that patch boxes were engraved on and off the rifle before inletting and after inletting! How is that for an answer, HA!
For real, I do think that a builder with the knowledge that Kuntz had was capable of engraving the box before inletting. From the original rifles that I have had the oppotunity to see the old builders used a much thinner brass sheet to make their patch boxes from than we tend to do today. It would make sence to me to fabricate the box, then engrave it while it was let's say the "flat stage". This could be done except the for the area where the box meets the butt plate. This area could be engraved after installation on the rifle. Because thin brass was being used it could be more easily conformed to the contures of the stock whitout damage to the engraving.
Braceletts are made this way today. They are engraved flat then bent to shape with little or no damage.
Now the key words there are the "Knowledge" to do the inlet well engough to inlet the box without any file work on the box.
I personally am not quite to that point. I have inlet some that I did very little file work on but I have yet to install one with no file work.
As far as engrave first then cut the box out, possibly on the side plates, maybe on the finial if the hinge is not intergal to the finial but I would not attempt to form a hinge on a nice engraved piece of metal, not saying it is impossible, just that I woould not attempt to do it.
I always pull any metal part off the rifle if possible to engrave it. It is just flat easier to do it that way. But I have also engraved on the rifle, again only if I have to.
The side plates on the John Jacob Sheetz documentary copy that Darrin and I did for the CLA auction this year are an example. I engrave them off the rifle, now the tricky thing is these side plates were nailed on the rifle, not screwed. So care had to be taken not to deform the side plates during the nailing process and not destroy the engraving. It turned out just fine.
You may ask why did I not engrave them on the rifle, because the original was done off the rifle. How did I know that, becasue the nail holes where drilled through the engraving on the original. This led me to believe that the plates were cut, shaped, inlet and then engraved before the nail holes were drilled then nailed on the rifle. Not an easy task to complete but doable with care.