Yes, in the case of rare (and many other distinctive) coins, it's often possible to reconstruct the pedigree.
Thanks to Google Books and especially the Internet Archive, many old auction catalogues are accessible in PDF and other formats. In the Internet Archive there is the Newman Portal full of old auction catalogues and even correspondence between numismatists and coin collectors and dealers in the mid to late 20th century. Usually, a prestigious collection will be identified by the name of the owner, and you can go back in time from owner to owner. But you have to be pretty good at searching in Google (few people are, in my experience).
In order to search that collection, the best is to go to Google Advanced Search and type
archive.org
on the line: site or domain.
I know all this because I have traced back the origin of a coin countermarked coin with large AD initials that were claimed to be those of a certain “Antoine Declos” in Trinidad. I was able to trace back the coin from the 2010s to the 1929 Guttag Auction in New York. There were five auctions of the coin in this period. It was truly fascinating to find out that the AD coin had been put together with two FD-countermarked coins back in the the 1920s, but for no good reasons. Then, someone in the early 1940s (Gibbs) speculated on the identity of AD ("Antoine Declos") based on the partially true belief that FD was a François Declos residing in Port of Spain, but the AD and FD coins had been put together by Guttag and then Gibbs (who had acquired Guttag's collection) for no good reasons.
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