But I doubt you’d have much success with dish-soap. I’m not sure what foaming agent is actually used to make foamed concrete. As a guess, what you want to make a porous concrete would probably be to make the concrete far more sticky by adding more lime to it, not detergent! Then, take some compressed air and fluff the mixture, blowing air into it somehow.
In any case, I think just having air-pockets wouldn’t be enough. You could try mixing in some water-proof but light additives. Like maybe adding styrofoam particles to the mix, say 30% or so.