App to change pitch of the sound coming out from the mac
I am not aware of anything that will do this task in real time as it requires some math to do the pitch shift. It is possible to take the alert sounds and process them to a different pitch like you said using an audio editor and then assign custom sounds, but an ongoing pitch shift would take some processing and I do not believe that there is a solution for that currently.

I have experimented with changing sample rates and the system adjusts for that and plays the proper pitch so it is not a simple task.