I'm not sure what you're asking. Why specifically World War II, and why rockets as opposed to any other type of payload? I think what you are really asking is would ordinance still on the aircraft explode if the aircraft crashed. If it did explode, then of course it would explode with as much force as if it had been dropped.

The vast majority of ordinance carried by aircraft in history, from World War I on, have had safety features and arming mechanisms. For example, many bombs from the World War II era, especially Russian and Japanese, have little propellers at the nose. This was an arming fuse, and the detonator was only primed for ignition once the propeller had completed a certain number of revolutions after the bomb was released. Others just used electrical timers to enable the detonator after a certain number of seconds after release. It was absolutely possible for aircraft to jettison their payloads with disarmed fuses in case of an issue with weight and fuel shortage, and this was routinely done in such situations.

Long story short, bombs, rockets, warheads, and explosives in general were specifically designed to only explode when you wanted them to. This not only applied to when the munitions were strapped to the aircraft, but also when in ammunition depots and ship magazines for storage. However, this could malfunction. If any sort of improbable collision or force set the detonator off, the weapon would explode. The heat from a fire after a crash might set the weapon off even if the detonator was safe. But on the whole, designers tried to make weapons as safe as possible to store and fly with.