yes. your bag might "disappear" if you leave it overnight.
can you change the SQ flight to a more godly hour?
otherwise, I vouch for the Ibis Budget hotel. used it myself and it was great. finding the shuttle bus pick up spot was a tough challenge though.
the airport is dead at night, and you waiting for a flight outside (you need to pick up your bag anyway) will be unbearable in the heat.