According to this paper,
Poor velopharyngeal closure will
affect speech but is not a matter of
great concern in regard to swallowing.
Now, if I read it correctly (entirely possible that I did not), then the velopharyngeal closure is a complicated way of saying "mouth". So getting something in there will affect your ability to scream.
Now the second part, can you get something in there not easily dislodge with a tongue? Hopefully this is easily enough observed that I won't get hit for references. If you open your mouth as wide as you can, you will observe that you can still pull it open more with your fingers (though it hurts) and when you release it will return to the prior gap. So yes, you can cram enough in there such that your tongue cannot deliver enough force to dislodge, though a sock may not be enough.