When globally installed packages are on the python path, and they conflict with the installation requirements, they are ignored, and not uninstalled.
When globally installed packages are on the python path, and they satisfy the installation requirements, pip does nothing, and reports that requirement is satisfied (similar to how global packages can satisfy requirements when installing packages in a --system-site-packages virtualenv).
pip will not perform a --user install in a --no-site-packages virtualenv (i.e. the default kind of virtualenv), due to the user site not being on the python path. The installation would be pointless.
In a --system-site-packages virtualenv, pip will not install a package that conflicts with a package in the virtualenv site-packages. The --user installation would lack sys.path precedence and be pointless.
To make the rules clearer, here are some examples:
From within a --no-site-packages virtualenv (i.e. the default kind):