If I had 3 cups of vodka straight, how long will it take to leave my system? Will it show up in a blood alcohol test?

24-48 hours & YES! 3 cups of vodka is about 24 shots - or 24 drinks and it takes roughly 1-2 hours for a drink to clear the averge persons body or longer for females. 3 cups of vodka at one time would most likely kill you or at least take you to the hospital with alcohol poisining & a pumping of your stomach. Don't do it!
That should be the. Least of your worries. If you are drinking 24 ounces of neat vodka at a sitting, you are clearly alcoholic. Whether anybody else finds out about appears to be your major worry, which i suggest should be the damage it is doing to your health and your life in general. That amount of alcohol will cause a bac of between 250-300 mg/%, which may be detectable for 24+ hours, depending on your liver.