During WW I, Pennsy moved heavy coal trains through NYP using DD1 side-rod third-rail electric locomotives. I never heard that it didn't work, or that the system didn't provide enough power. In those days the Pennsy generated its own third-rail juice from the recently demolished coal-fired power plant in Long Island City.
Doubt it would work today, though, simply because of the increased train traffic in and out of NYP, what with LIRR, Amtrak (including NY State service) and NY Transit all squeezing their trains into a station without sufficient capacity.
Fairbanks-Morse forever!