After a night of drinking hard alcohol and not urinating during the night or in the morning, given a sufficient amount of time has passed for the alcohol to have been completely metabolized by the liver, will a single urine test the following day show an accurate presence of alcohol?

Not sure I get the wording of this... if you're asking about if you can drink the night before and then take a urine test the next day and pass... no. Not going to happen.

I don't understand what the whole thing about not urinating all night has to do with anything though.

What happens if you FAIL ?