Afternoon thundershowers are pretty normal in the summer along the JMT. Most of the time they're no big deal and clear out in time for you to have a dry camp.
However, one time when I was coming over Pinchot pass, the storm lasted for hours and was quite severe. We still had a dry camp, but we also had several hours of sopping wet misery.
Also, on Labor Day weekend (yes, that's not August but pretty darn close), we had two nights of rain/snow in the Piute Pass/Evolution Valley area. Pretty miserable quite frankly. All we had was a plastic sheeting tube tent. Light but not able to handle heavy rain.
Chances are, something light will do just fine, but there are times where it will rain at night in August. I think in the last 35 years, I've had a seriously rainy night maybe about four times.