Figured it'd be useful to have a topic devoted to this, since it comes up fairly often.
The usual contention is that since the Royal Guard Champion doesn't technically activate abilities like Quick Draw and conditions like Weakened don't affect him.
So, I fired off an e-mail to FFG and this is the response:
So, it looks like the Royal Guard Champion does activate for the purposes of Quick Draw and Weakened.
Thought it would be a good idea to post this here, for future use.