Yes, this is possible but be very careful - querying the db isn't necessarily recommended because if changes are inadvertently made to the db it may cause corruption. Always check to make sure you have a recent db backup:
$ cd /OMERO/OMERO4_4/db_backup/
Look for a recent .pg_dbdump file.
For example if I wanted to run an sql query to list all of the active users and the screen, plate and group (owner) association I'd use the following steps :
Connect to the omero database (columbus user):
$ sudo su columbus
$ psql omero4_4
> select e.omename as user, s.name as screen, p.name as plate, eg.name as group from screen s join screenplatelink spl on spl.parent=s.id join plate p on spl.child=p.id join experimentergroup eg on eg.id=p.group_id join experimenter e on e.id=p.owner_id order by e.omename, s.name;
The output would look something like this:
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RAH