Is it normal for condensation to drip without the HVAC unit running?
Yes it is normal for condensate to drip for a while after the unit runs. If you have a steady drip for hours it is possible the drain is partily plugged and the tray is filling up cleaning the drain line is required to fix this. If there is a steady flow for a long period it may be the evaporator is icing up from dirty filters or low air flow across the coils. The last possibility is a incorrect Freon level usually a low level will cause ice on the evaporator but an overcharge can also cause this but this is less common now with licensing required to service Freon based systems.