That really depends on the paste. If it has ground-up metal bits in it (and not metal oxides which are ceramics), then the alternating conductor and insulator makes it capacitive. Silver is the oddball, in that the oxide is even more electrically conductive than the pure metal! So silver oxide in paste is also capacitive.
As you'd expect, a compound that can store an electrical charge and release it abruptly is generally a bad thing to have bridging a whole bunch of sensitive electrical traces--though the voltages may be low enough to not matter. If you look at the datasheet for the socket or CPU you will see most of the pins are redundant for power or ground, and having paste across any of these would be fine. What you probably want to avoid is paste connecting any data pins, and especially not both power and data pins.