No, the drug still has to be processed thru your body before it makes it to your urine. Whats in your urine is just what your body has processed thus far. Even if you urinate a lot it doesnt speed up the process.
Not totally sure but I seem to remember drinking a lot (but not crazy amounts, you can do harm that way if you really go overboard) IS advised to speed things up.
So indirectly I guess it does help.