No, urinating will not make you less drunk. When you are drunk, the alcohol that you have consumed gets into your bloodstream and affects your physical and mental control. This is why we use blood alcohol level to determined how impaired a person is. Once alcohol is in your bladder, it is separate from your bloodstream so it does not impact your physical or mental state.
Some people may feel better after urinating when they are drunk and this might make them think they are less drunk but it is just an illusion. The only real way to sober up is to let time pass and allow the alcohol to leave your bloodstream.