Yes it will leak, and quite a bit at that! Water runs down through the opening via the cowl. Be careful because it will make the carpet damp and when the evaporation process happens it can cause surface rust inside the vehicle on bare metal or cause mildew.
The best way to see for yourself is to stuff a towel in the kick panel hole and run a hose in the cowl very briefly, the water will drip from out of the kick panel hole.
What i'm doing as a temporary measure is putting large towels in the kick panel holes and letting them hang out a bit to grab the drips, and covering the cowl with a waterproof tarp. If it rains or you suspect the towel might be wet trade it out with a dry one because the towel holds moisture the same way the carpet would and cause surface rust/mildew.
I'm still working on mine but i'm determined to get an everlasting-super tight seal on the kick panels so they dont have to be removed for a lifetime =)