lucy24 - 12:12 pm on Aug 1, 2013 (gmt 0)
Having noindex within this HTML that is sent alongside 404 response is obsolete and will not speed up Google removing the original page out of its index.
On the other side, putting noindex in HTML that arrives with 404 response will do no harm, so if you prefer, you can do it but it will make no difference whatsoever.
The only way I can get these two lines to make sense is if I read each one as meaning the opposite of what I think it was intended to mean :( (I also can't figure out what word your brain was aiming for when your fingers typed "obsolete", but that's minor.)
Are the two bits I've bolded the same thing or different things?
Either way, my own perfunctory experimentation suggests that g### does not, in fact, index the 404 page. They may not even read it; once a robot has seen the 404 it can choose not to look at the accompanying HTML.