Hi Lex,
It can be done
theoretically
but there are many problems. Some researchers have tried to do this with e.g. the Roman Republican coinage. The main difficulties are:
1) How many coins did each die strike? Were all dies used until they fell apart? Were they retouched? Were all dies used for irregular coins of iron like official coins? With some types of coin, e.g. official issues in gold, only a few presentation coins might have been needed and then the dies destroyed.
2) All these clearly affect estimates of how many coins were struck per die. Eventually, let's assume we arrive at an estimate of how many coins an average die might produce. How many coins do we need per die to begin to estimate the total number of dies? Numismatists still argue on this as well.
3) Copper alloy imitations are often in a very poorly preserved state compared to silver denarii on which most die-studies have been done. This makes die-studying harder.
4) Locality. If some locally-produced imitations only circulated in a local area and that particular area has not been searched or has changed significantly since, the picture will be skewed. E.g. Parts of the Norfolk coast in Britain are nothing like they were in Roman times
5) There are so many of these coins! I have got lots of die-identities but it would require many many more coins for me to believe I am even getting near results. For example my Mint II Style 1a types - out of something like 60 coins (up to about last year) I had 57 dies! The coin populations are so large

These are only a few ideas I've thought up early this morning while half-asleep. I'm sure other readers will have plenty more to add.
Regards,
Adrianus