No, you don't want to remove it. Are you absolutely certain that you will
never want to install any software [easily] again? Do you want to go hunting
through the Ubuntu archives for .deb packages hoping you won't stumble on a
non-free one and install it?
Even if you somehow magically will never need new software ever again, you're
out of luck. As I understand it Add/Remove Applications is an interface to
the Synaptic Package Manager. So trying to remove it would be like trying to
slice a pair of scissors in half using only that pair of scissors. There are
ways and means to get rid of it, of course, but do you really care to hunt
through the maze that is the file system structure of GNU/Linux and find all
the related files?
