If you get a speeding ticket in Pennsylvania- and live in NJ, will NJ
Motor Vehicles get notification and will any applicable points be
transferred?

i know from first hand experiance that tickets recieved in states
other than you own can appear on your driving record. i know Ohio,
Virginia and Maryland will report them. i am sure Penn. tells
Maryland, but i dont know about NJ. Logic would say they do. Ask at
the DMV. they might know

Many states have reciprocal agreements in this regard and share info
amongst each other.

An example I have is:

I had a Florida drivers license when I joined the military and was
able to keep it through out my career for the next twenty years.
Sometime during that twenty years, I got a ticket in North Carolina
that I had no intention of taking care of (I had no plans to ever be
back in NC). Anyways, when I got out of the military I "retired" in
Texas. I got a license from them and thought all was good. I ended up
receiving a letter from the Texas DOT statingthat I had an outstnding
ticket/warrent in NC and my Texas license would be revoked if I did
not take care of that ticket within 30 days.

So, while you may get away with it for a short period of time (almost
thirteen years in my case), it will probably catch up with you
later...