Minecraft Alpha, Classic, Survival Test versions

Are you saying it is possible for some of the versions we now consider lost forever, to at one point have been available on archive.org, but have since been deleted?

I highly doubt that. Archive.org is so strong in support of the concept of archiving online content, that they would likely demand proof that the DMCA takedown request was legit (to make sure sure that it isn't just some troll sending it), before complying. Furthermore, they are often seen as a museum by others, preserving digital history, more than as a piracy site. As such, even content owners like Mojang are less likely to send DMCA takedown notices to start with, and more likely to to send DMCA takedown notices to sites like Medafire or Mega, sites which are often seen as promoting piracy. In fact, archive.org is considered to be so reliable at protecting uploads for the sake of preserving digital history, that the Minecraft archiving community Omniarchive on Discord, uses archive.org to host rare jars that they have found.