We did this in April-enjoyed the pool until after lunch and then went to the parks staying until we were ready to leave.
Sorry, huge difference between arriving late-morning in April and arriving late-morning in August.
To OP, the simplest answer is for you to try it, see how it goes, then make adjustments as you see fit. Much depends on the weather you happen to get, and how you personally react to it. You both might react well, or you might collectively decide to adjust your approach after you experience the trade-offs of sleeping later.
Since you are asking, touring during thunderstorms = a significant trade off. A number of rides shut down, especially at AK. No EE, no animals, no P Whirl, no Triceratops Spin, no Kali, and NO swimming in the pool. It also can be a bit daunting to move around WDW during heavy downpours. WDW gets deep puddles that are 2-3 inches deep and so wide they are unavoidable. Also important to know: shuttle boats stop running.
In August, you simply can't expect to be able to go swimming every afternoon. (Then again, you might also get lucky.)
We've been to WDW many times, and we've tried every approach. Our technique might not be yours, but for us, we find it best to make seasonal adjustments to how we tour. Our SPRING approach is different from our WINTER and SUMMER approaches.
For us, SUMMER = early (for a few early hours?), take a break, return 5pm-ish/post-storms, and stay until park close/we feel like leaving.