No, you should not hunt in a thunderstorm. Here's why:
Thunderstorms are dangerous because of the lightning. Lightning can strike anywhere, at any time, and it doesn't discriminate between humans and animals. In fact, according to the National Weather Service, lightning is one of the leading causes of death from weather-related hazards.
Lightning can strike up to 10 miles away from the center of a thunderstorm, so even if you're not in the direct path of the storm, you're still at risk. And, if you're in an open area, you're even more susceptible to being struck.
Thunderstorms can also bring high winds, which can knock down trees and power lines. These falling objects can injure or kill hunters.
In addition, thunderstorms can cause flash flooding. This can make it difficult to get to safety, or to retrieve any game that you may have killed.
So, bottom line: it's just not worth it to hunt in a thunderstorm. Stay safe, and wait for better weather conditions.