Is it possible to tell you've been smoking marijuana by examining your throat/mouth?

Yes. Possibly your teeth will show a discoloration and some left behind tar. Also, if they are examining your mouth they probably will have a mouth swab in one hand and asking you to put it between your teeth and inner cheek to test for drugs. The THC in pot resides/accumulates in this tissue and is easily detected with a mouth swab.

And if you just smoked it, the pupils of the eyes.