BTW, I imagine a pitot tube placed on the body of the engine would not need extra heating and would be very unlikely to ice. You can even place it inside the exhaust and compensate the reading for engine flow.
There are such things in the engines! They're used to feed the data about engine performance to FADECs (http://en.wikipedia.org/wiki/FADEC) and the crew.
But they're totally useless for airspeed calculation! Bear in mind that air flowing trough and around the engine has totally different dynamics than the air passing around the rest of the airframe. Well, that's kind of the point of the engine - to create thrust, isn't it? That's why airspeed, altitude and AoA sensors actually have to be placed further away from the engines - so that they give as accurate picture as possible.