If I took about 3 to 4 mg of Suboxone on sunday about noon. Would it still show up on a urine drug screen thursday about 1 pm?

Depends on what test. The likelihood is low that one dose of 4 mg would show up 4 days later on a drug test, but it depends to some extent on exactly what test they are doing (a screening dipstick test or a formal gc/ms test = much fancier and more sensitive). More important than beating a drug test is dealing with your issues. Your success will not be measured in hiding your problems, but getting help dealing with it.
Yes. Yes, it will show up in the urine drug screen if they test specifically for it. Suboxone is a combination of buprenorphrine and naloxone. The half life of suboxone is about 24-72 hours. Usually, it takes about five half life before medication is out of your body.