Change Joomla User Group After Registration
Yes, you can do it by way of CiviCRM groups.  Two parts:


Create a CiviCRM group for each profile. Go into the advanced settings for each profile and select the corresponding group to have all contacts filling the profile automatically added to the group.
Install the CiviCRM Group Sync extension in Joomla. Configure it to sync up the appropriate CiviCRM groups to Joomla.


An added benefit is that you'll be able to filter by the groups within CiviCRM.