It depends on what they check for and how in depth the testing is. Most likely no as Naproxen is used in a lot of OTC anti-inflamatory and pain medication. I wouldn't eat a poppy seed bun the night before the test though.
Will A Naproxen Show Up On A Drug Test?
Yes naproxen will but it is no big. Naproxen is the same as aleve which is available over the counter. All you need to do is list it as something you have taken. No prescription needed.
No it will not I have takin it for years due to a car accident and have never failed a test and I have even takin a hair follicle test and nothing has shown up, but do beware of stackers they will cause you to fail for opiates