No not on my plants, but the bottom leaves will die when the heat gets high. My plants are over 6 feet & new growth is growing horizontally with blooms & green tomatoes.
But the bottom leaves are brown & dried up.

While there is no reason to leave dead branches on a plant there is also no reason to remove branches that are not dead. That holds true regardless of where they are located on the plant. The one common exception is removing any lower branches that are in contact with the ground.

Do branches below a ripened cluster automatically die? No.

Dave