You don't have to have the GPS plugged into your PC for Basecamp to work. But you do have to have an up-to-date map loaded on the computer for Basecamp to work.
I use Basecamp all the time to create routes to load on my GPS. But I use Street Atlas to plan my routes and then recreate them in Basecamp to upload to the GPS. The main issue I have with Basecamp is that the smaller roads disappear as you zoom out. That makes overall planning a real pain, and is why I use Street Atlas for initial planning.
Like someone mentioned double check your route after loading it on the GPS. Some of them are notorious for changing the route.