"Yes it is possible. Follow these steps:
To run your script as another user as one command, run:

/bin/su -c ""/path/to/backup_db.sh /tmp/test"" - postgres

Breaking it down:
 /bin/su : switch user
 -c ""/path/to..."" : command to run
 - : option to su, make it a login session (source profile for the user)
 postgres : user to become"