I for one used to do this a lot. Get in at 11:45 PM, go to the transit hotel, sleep for 6 hours, get up, clear immigration and customs, go to the Conrad or Hilton and check in at 7 AM (early check-in), enjoy breakfast.

It gets a little dicey with checked baggage; I guess your bag goes round and round then your carrier pulls it and puts it somewhere. In SIN I wouldn't be worried, just go look for your bag in the morning?

Even if the transit hotel is booked full just go by wither/both and inquire. A lot of people make reservations and don't show as there is no penalty.