Knowledge Base - Needed data to Geocode
"Can the configuration only require City, State, Zip/Postal Code, and perhaps Country?"
Yes, the user profile can contains all informations, like City, Zip, Street, Country, ... and you can configure Geocode Factory only with City or Zip code.
If you goal is to preserve the user privacy, you can use the Accuracy setting, to show the markers. Then the user's coordinates should be perfect, but the marker is placed randomly in a radius from 100 to 500 meters. This is the better way because you can use the right coordinates for another usage like radius search or what you want.
Geocode Factory 3