From my experience, Unity runs fine from a USB drive if you copy the installation directory from Program Files. It doesn't seem like the installer needs to write to protected locations. Why, then, does it insist on having admin rights to install?
Why can't I choose where to install Unity to and then have the installer decide if I need admin rights based on that location? (I.e., if I were to install to Program Files, it would require admin rights, but if I were to choose a non-protected location like Documents, it would not.)