This is a little more complicated than you would think and there is an old thread on it.
"Generally" an independent PTO is activated without the necessity of using a clutch and is not affected by the clutch. A live PTO is often activated/deactivated by a two stage clutch in which you can depress it half way to shift gears without disengaging the PTO. In a non live PTO, engaging the clutch with disengage the PTO.
I am sure someone else will be able to provide more detail with the exceptions.