Generally speaking, user searches CAN work without SOLR, but it depends on the search input / query. Alfresco actually has some semi-smart internals to determine when a query can be executed against the database (not requiring SOLR) and when not. Additionally, user search in particular also has some specific handling to switch between DB and Full Text Search.
Generally speaking, if you only query for a single term, i.e. "afaust" (user name in this case) then that search should use the DB and not require SOLR. If you start searching for multiple terms i.e. "axel faust" then that search will have to use SOLR, since Alfresco can no longer assume a simple, straight forward exact match search on a few properties (user, first or last name), but has to take in any constellations (i.e. combinations of each of these fields or partial matches in only one field...). User search also allows you to specify yourself what you are searching for, i.e. "userName:afaust" instructs Alfresco to only query for user name, and in this case the DB can be used. Alternatively, "firstName:axel AND lastName:faust" specify which input needs to match which field(s), and with that in mind, Alfresco can again use the database instead of requiring SOLR.
