In a hangout from this morning, Google's John Mueller was asked how Google handles a page that you applied a canonical to but also has a noindex on it. Does that page pass the noindex. You can see how the question kind of caused a lot of confusion. The short answer is that Google in practice generally just assumes in these cases the canonical is a mistake and ignore it.
The question came up at 4:51 into the video. Here is the video embed followed by the transcript:
Question:
I was at a seminar the other day and they said if you apply a canonical and a noindex on that page, the canonical will pass the noindex to the canonicalized page. Is that the case?
Answer:
Um. Thats. I don’t know. It is something where we kind of discussed this like a long time ago, internally at least, with regards to what we should be doing in a case like that.
With the canonical you are saying these two pages should be treated the same and with the noindex you are saying this page here should be removed from search. So our algorithms theoretically could get confused and say they should be the same and this one should be removed, so we should remove both of them. Right? Or they could look at them differently and say that these should be the same, and this should be indexed, therefore maybe, I don’t know, what should we do with the noindex here.
But in practice what we have kind of come to is just saying well probably the rel-canonical is a mistake. Probably you are just using the noindex as a way to kind of pick a canonical or force a canonical. And from our point of view web ill try to follow it like that.
Forum discussion at YouTube.