Ok, firstly, it's possible to cough under anaesthetic. It actually happens quite often, especially on the way to waking up, and sometimes intra-op when a person is 'light' (but still unconsciouss). Now, for delicate procedures, like the one you just mentioned, anaesthetists paralyse patients for the duration of the op, then reverse the paralysis at the end, for exactly the reason you mentioned - we don't want a person coughing while the surgeon is manoevering around your jugular vein. A funny thing is, that some drugs that put people to sleep actually cause transient hiccoughs (after the patient is asleep).
66 mths ago