Can a get (bill of divorce) suffice as evidence of proper gerus (conversion), assuming one was born a non-Jew? If so, under what circumstances? For the man or for the woman (or both)?
I am not sure if Halchically a get should be a proof of conversion, but I can tell you that in practice the Rabbanut will not even except their own divorce certificates as a proof of Jewishness, forget about its being a proof of conversion.
When I remarried in Israel I presented my divorce certificate as proof of Jewishness. The Rabbanut did not accept this document. They explained to me that in order to avoid Agunot they will always write a get with no questions and without verifying anything, so it cannot be used to prove anything.
(I have been wondering since then how they let my wife remarry based on the same certificate. I guess its one of the mysteries of Judaism.)
One never has a Get to show, only a Ptur. The language of the Ptur follows the language of the Get but might include some information in an addendum. If the Ptur was written by a well-known Posek and includes information about the Ger/Giyores then perhaps this information would be accepted by a Bet Din. If however, the Ptur does not include any additional information and the rabbis signed on it were not known to be meticulous, then perhaps other rabbis would not be as likely to accept it as a first-hand document. At all times, one is responsible for the evidence of her/his conversion, both the physical document and the "proof in the pudding" by how one dresses and acts.