No, unfortunately they will not. You are right about the transit passenger being able to enter and leave Singapore (once) during their layover. But the only way for you to do this would be if you were in transit as well. If you're REALLY REALLY keen to do this, you could book a quick return flight to SG earlier that day, and meet them at arrival gate after your return flight arrives. That way, you'll have two tickets to prove your reason for multiple immigration checks.