Rainfall in any form will provide some drought relief. A good analogy might be how medicine and illness relate to each other. A single dose of medicine can alleviate symptoms of illness, but it usually takes a sustained program of medication to cure an illness. Likewise, a single rainstorm will not break the drought, but it might provide temporary relief.
A light to moderate shower will probably only provide cosmetic relief; its impact is short term. Thunderstorms often produce large amounts of precipitation in a very short time, so most of the rain will run off into drainage channels and streams rather than soak into the ground.
Soaking rains are the best medicine to alleviate drought. Water that enters the soil recharges groundwater, which in turn sustains vegetation and feeds streams during periods of no rain. A single soaking rain will provide lasting relief from drought conditions, but multiple such rains over several months might be required to break a drought and return conditions to within the normal range.