2002 Ford F 150 with a 2.3 if you disconnect the terminals off the battery will it still runs

Some cars will... some won't but here's the danger of doing that. The truck may lose all regulation of the alternator output causing an unregulated over voltage through your system. (Crispy Critters syndrome) Most cars rely on the snubbing effect a large battery will provide if subjected to over-voltage ... be careful and remember that electricity travels at the speed of light and that's a whole lot faster then you can turn the engine off if you see a problem