Short answer: no. What we consider "coinage" began in the sixth century B.C., with King Croesus of Lydia.
Typecasting didn't happen for more than a thousand years thereafter.

I think all engraving for casting or impression can be, in a way, practice for punchcuttery. Seals, dating back to the mess in potamia were produced in limited editions for official use, until metal became less precious, and note they used one of the less precious metals once they started making type.

But minting, gun, and other weapon making, and gold smithing, we know were all related to early famous type designers. Near the end of punch cutting, at least in the U.S., founders were based in places where there were significant clusters of industrial engravers and machines were made, like Milwaukee, Chitown, St. Louis, and the industrial centers of the northeast. In Philly, NY, and Boston, they made coins too.

All these places and more, had people skilled enough, e.g. to make very tiny parts for early watches, and kinds of less tiny but still very small gears and nuts and bolts... You know parts, and every one of those parts, started on a drawing board, ended with a master drawing, and proceeded to production to tolerances reaching 1/10,000 of an inch by 1900 or so.

By then bridges, telegraphs lines, and a few inside inventions, made the Linotype machine go viral, and that changed a lot. Whether making coins breeds type, great great great grampa, I'm thinking.

The connection between coins and type is that the minting of coins was a pre-existing technology that used letter punches in the making of coin dies. Whoever introduced the use of letter punches and matrices into typefounding was probably inspired by the letter punches used in making coins, but it's worth noting that the styles used were different. Early type was usually bastarda or textura, whereas the letter punches used on fifteenth-century coins in Latin Europe were normally lombardic.

If Needham and Agüera are correct that Gutenberg wasn’t using punches and matrices, then minting technology contributed to a subsequent improvement of Gutenberg’s technology, not to its initial creation.

But, if you agree with that research, then what Gutenberg couldn't do from minting technology would not need contributions from minting technology in the subsequent improvement of Gutenberg’s technology. :)

One web page giving an account of their research said "The scholars said they discovered that individual letters differed in shape from one another in such a way that they could not have come from the same metal mould. For example, the ‘A’s, ‘B’s and so forth on any given page on Gutenberg’s papal bull are not always exactly the same shape."

I really hope this was garbled. Scholars of printing long knew that Gutenberg had two forms of each letter, to simulate the effect of a hand-produced manuscript with movable type.

If Needham and Agüera actually discovered that there were many more than two forms of each letter, so that Gutenberg really printed from, say, hand-carved wood blocks, contrary to popular belief, that would be a major discovery. If, on the other hand, they jumped to their conclusion because of the two forms of each letter that were already well known, because they put a magnifying glass to Gutenberg's Bible without doing a literature search beforehand...

EDIT: A fuller account, at

http://www.open.edu/openlearn/history-the-arts/history/history-science-technology-and-medicine/history-science/the-discovery-changed-our-view-gutenberg

is now leading my thoughts in the direction labelled "deliberate hoax", rather than the previous conclusion of "unutterable stupidity".

This is because

"To their surprise each letter in its many reproductions on each page varied, even though they could find identical repetitions of that letter on other pages."

So either Gutenberg still made use of movable type, even if by cutting up his woodblocks into pieces to re-use the letters (one can't really say he invented it, of course, thanks to Pi Sheng)...

or, instead, we are in error to think that Linn Boyd Benton originated the typographical use of the pantograph!!!!

And if that's true, then all I've got to say is

♫ God didn't make little green apples,/and it don't snow in Indianapolis/in the summertime ♫

For another musical selection, connected to cutting-edge research on the history of technology of apparently similar quality, go here:

https://www.youtube.com/watch?v=YhwkdJfsAKg

At least the music was well done...

Oh, wait; I am being too harsh. If Gutenberg did invent/use movable type, but not punches and casting molds, then perhaps they were merely claiming that Gutenberg used individual hand-made movable types. That would explain no two letters on the same page ever being identical, which is what they claim to have seen.

The Press has been known to badly garble the results of research before. Or it is but my own failing in not reading the post mentioning them more carefully, which did speak but of punches and matrices, although the web articles I found spoke of movable type itself.

EDIT: Searching for images of the pages of the 42-line Bible led me to this more conventional research,

link.springer.com/article/10.1007%2Fs10032-010-0140-6#page-1

which claims the use of multiple matrices for each letter as a recent discovery, rather than something that was long known. The paper dates from 2010, and I thought I had seen the alternate forms of Gutenberg in books on typography from the 1970s if not earlier.

Check out Albertus and its lineage.

hhp

What Needham and Agüera y Arcas claimed was that Gutenberg’s movable type was cast using a one-use method such as sand casting, rather than in reusable matrices.

In the Report of the Maine Press Association for 1883, I found the confident assertion on page 9:

Up to 1450, the types used by Gutenberg were cut by hand in wood or metal. At this date Peter Schoeffer invented a process by which types could be cast, and which constituted one of the most valuable improvements in the history of printing.

Another book gave a wide spectrum of claims. Typographia noted the specific credit for type casting was given to Schoeffer by papers left by Fust, and that this book

http://www.smu.edu/Bridwell/Collections/SpecialCollectionsandArchives/Exhibitions/PeterSchoefferPrinterofMainz/EarlyMasterpieces/Durandus1459

which indeed came after the 42-line Bible, was the first one set with the new-style cast types.

The book Counter Punch by Fred Smeijers is a good read on this subject. Fred is a type designer and his father was a silver smith who was used to work with stamps / punches. Fred also did several research projects on the process of punch cutting at Plantin-Moretus.

https://hyphenpress.co.uk/authors/fred_smeijers
https://hyphenpress.co.uk/products/books/978-0-907259-42-8