There is absolutely no problem to work with both apps at the same time, git repos are juste folders on your computer and both apps simply show you in a visual interface what your repos look like.
For example if you make modification on your local GitHub repo using the GitHub app and you then open this same repo with SourceTree, you'll see every pending modifications you made with the GitHub app.
There is only one index for each git repo, both apps will read the same index and show the same information. The modifications made on one side will be visible on the other side.
Hope this will help you.