Since the welcome notice is time sensitive (if I remember correctly), pressing resend in notices.pl should not resend the same content, but should generate a whole new one. Unless someone smart already addressed the time issue and I am just making stuff up.
I am not sure if I understand the issue. You can send a new notice anytime from the "More" menu and htey are sent out immediately (no delay through message queue processing).
You know what? I was confusing this with the verification email. My bad. Ignore me today.