Personally, I dont sanitize my hydrometer. I like to handle it too much to be able to leave it in a fermentor. I get the beer using a sanatized measuring cup then pour into the tube. I always spin the device into the tube so the CO2 bubbles from fermentation don't give me a low reading.
I don't see any reason why you couldn't leave it in there, just the prodecure I use to get my readings would keep me from doing it.
PS i forgot to mention that I drink/toss any sample I use to get a reading so the beer from the unsanitized hydrometer doesn't go back into my fermentor