Is is possible to create a web app using yeoman (yo, bower, grunt) WITHOUT having git version control or is this mandatory?
Yeoman doesn't have any hard dependency on git (or any vcs for that matter).
That being said, some generators might rely on git. So I cannot guarantee every generator you'll use will work if you don't have git installed.
The same is true from Grunt, it doesn't rely on git, but some plugins might.
Bower on the other end relies heavily on git to fetch packages. So if you plan on using Bower, then you need git. Your project is not required to be on git, but git binary needs to be installed.