If I use an embeded google map in my website, will the data contained in an kml displayed be publicly viewable?
Will it be possible for the user to access just the data displayed (i.e., not the user interface) or would I have to provide that separately?
No, the data will not be public. I'm not sure about your other question though.
If you load your KML through the API, with GGeoXml(), (V2), or KmlLayer(), (V3), then your data needs to be in a public server because it is parsed by Google's servers and they need to be able to get to it. If you load it with a third party extension then you can keep it private.
Third party extensions that can load and parse KML data are EGeoXml() by Mike Williams
http://econym.org.uk/gmap/extensions.htm#EGeoXml
and GeoXml() by Lance Dyas
http://www.dyasdesigns.com/geoxml/
but I believe that both of those are only available for the API V2 for now.