The short answer is: No, you can't.
git repos and Ubuntu repos are quite different.
git repos in most cases contain software sources that need compilation.
Ubuntu repos contain deb binaries that can be directly installed to Ubuntu.
There are some exceptions. git can contain binary files and some deb packages can contain sources that are compiled by Ubuntu, e.g. DMKS ones.
But still they are very different and there is no general way to "install a git repo as an Ubuntu repo".
Generally speaking, you'll need to do git pull on a git repo to update the sources and then compile the program each time you want to update unless you create a script that will do it for you automatically.