If I consumed three 8oz wine coolers with 8 percent alcohol by volume at 10:00 pm would it show up on a urine test the next day at 3 pm??

Quite possibly.
What happens if it does ?

I'd say get ready to fail. Or buy a lot of lottery tickets right away if you don't.

Alcohol is metabolized by the body at the rate of approximately 1 standard drink every hour (if you want to be safer, you can use 1 1/2 hour) If you were to drink 3 standard drinks (14 grams of pure alcohol, each), the alcohol would be eliminated in approximately 3 - 4.5 hours. Urine produced AFTER this period would be negative for alcohol. (You need to remember that urine that was produced during this time would still have alcohol if you had not emptied your bladder after this time).

Essentially, except with exceptionally heavy alcohol consumption, a urine alcohol test done 12-24 hour later would be negative.

However, if the test includes the EtG testing, this can detect recent alcohol use for 26-80 hours depending on which reference you believe.

Short answer - if it is a standard UA for alcohol, I would expect it to not show up. If it is an EtG test, I would absolutely expect it to show.

I would expect last nights drinking would be detected by a urine test but at what level is the question. To many factors involved to be absolutely certain.