No, the Radius Search Plugin requires proper latitude/longitude data in the entries to function. The SP-Geo field plugin will automatically do this when entries are created. However, Geocode Factory will also perform this function.
Therefore, you need the SP-Geo field plugin and/or Geocode Factory installed.
If you don't have either of these products, the Application will not work because you don’t have proper lat/lon data. If there is a demand from users to allow this application to work with custom latitude and longitude fields we may consider adding that functionality in the future, but currently it works only with either the standard SOBI Pro functions or with Geocode Factory component.