I have two projects within my solution, for this example I will call them project A and B.
Project B references A. Can Project B access the app.config properties of project A?
I wish to access an app key string within the app.config of A.
string tfsUri = ConfigurationManager.AppSettings["TfsUri"];
That's generally not a good idea, as you introduce hard dependencies between the projects. So if you can copy-paste config value, that will make your projects self-contained (however, this introduces duplication of config value).
You can also automate this, so that when you build a project the configuration dependency is automatically resolved.
Having-said this, there are other options, and in each case you may prefer to use something else. Your other options are: