is it possible to search for user names with solr?
Regarding the Content Profile module, as long as anonymous users have access to view the profile nodes, the content should be able to be indexed by Solr.  You can use the Automatic Nodetitles and Token modules to ensure that the username is set as the Content Profile node's title. You might want to set the field bias for the title to a higher value so more importance is placed on it when ranking search results.

Normal users probably can't see the core User search because they don't have the "access user profiles" permission.  If they are granted that permissions they should be able to use the core User search.