Its 24cm depth. Should be fine. Seen people using 21.5 depth cases and they had their props on. What the dimensions of the case you recommended?That case looks as if you will have to take the props off every time to fit it in the case. Look for one of the atomicrc or red rocks cases on amazon. They are usually under $100 and are some of the best cases for the price out there. and the are big enough to not have to worry about taking the props off over and over. Tho some of them still need to have a tiny bit of foam cut away to fit the remotes tablet holders even for the ones said to be for the p3s BUT thats super easy to do. all you have to do is set the controller in the slot 1/2 way till the tablet holder is resting on top of the edge of the foam and then use any sort of sararted knife Like a steak knife to cut around the profile of the tablet holder and in less then 20 seconds you have a perfect custom fit case.
oh and btw Id get one in silver instead of black. Being black cases will get hot in the sun ware as a silver case will reflect a lot of the sun light and not heat up as much.