Well, I guess the doctor might not know, but it's more than likely he will. The reason is that the most common cause of voice loss for a common illness (Ex. cold/flu) is mucus in the throat. This is visable to the doctor when you open your mouth and he shines his light down it.
I have a diff. idea to get a doctors note. Say that you are having severe sinus pressure, however not too much mucus is dripping down your throat. This would be the reason that there isn't much mucus in your throat, but your voice is mildly gone. Tell him/her that the pressure is causing dizziness and you get unbalanced sometimes and your vision gets blurry. Also, the Day Quil you have been taking to relieve these symptoms (or even Dramomine which has known sedative effects) makes you tired. Due to this, you need a doctors note because I am guessing with whatever you are doing, dizziness is not a desirable condition to have.
I find, in general if towards the end of your appointment you just say, "I was also hoping to get a note because I have to ______ and I really don't think it's a good idea for me right now", they hardly ever say no!