The answer is, 'No.' Not possible...not even from a whole box of pencils.
Why not? Because there is no lead in a pencil.
Yes, it is called 'pencil lead' but what it really is is graphite, a totally different substance from lead. Graphite is not a metal, but a mineral formed from carbon.
The graphite used in pencils is more or less harmless, as the New York Times explains.
So, getting stabbed with a bit of pencil lead, or swallowing some, is not going to give you lead poisoning. Of course, there would still be a hole in you from the stabbing, and swallowing bits of wood and other foreign material is a choking hazard, as well as a threat to your digestion.
Probably best just to use your pencil for writing.
(On a related note, you also cannot get ink poisoning from a pen.)