Should I use Git for deployment of web apps?
This seems like a nice way to do things. If you're tagging and branching properly it will enable you to quickly switch back to working versions of your site too in the event that something breaks.
I think this is a fine way to do it. I handle things in a similar manner, where live sites are just a checkout from the repository, and i update them as necessary.
Git is fine but you can do a lot better then just using git pull. Take a look at railess deploy for capistrano.
Capistrano basically does a combination of rsync and git pull to deploy copies of your website. It supports roleback, staging and distributed deployments.