From experience: the two web-apps are entirely isolated from one another - the libraries for one are not utilised in another - thus to answer your initial question - yes they would be loaded twice.
To answer you second question, whether you should deploy these libraries into Tomcat's shared directory - I would say no, and here's why:
If you deploy a library Jar into the shared location (tomcat/server/lib), then that version of the library becomes the default for all web-applications running under that instance of Tomcat. As you can see from this overview of the tomcat architecture, the class-loader works "down the chain", with an individual web-app's lib folder being the last place it will look before it throws a class-not-found exception.
The problem therefore of deploying a shared library to that directory is that it breaks the architecture for individual applications being isolated from one-another. Fine in your initial example, but if you want to deploy a third-party application (e.g. if you a running an app that consumes Portlet's to handle specific content), you instantly run in to version dependency issues - your shared version of a library may not be correct for the third-party application, but because the package is already loaded, you'll throw exceptions left right and centre.