This topic was about GCM specifically, which, since it goes through Google servers (unlike, say, my arbitrary browsing, or the network profile of my arbitrary apps), is directly available to Google.
Speculating that Google may have access to my full network profile is a little off-topic, but yeah, if they did have that data, they could certainly do similar analysis on it.
The answer is "GCM may reveal more to Google than one would expect from using an E2E encryption application (like metadata, and more than one would initially assume)".
The person I initially replied to was talking about Google, GCM, E2E encryption, and that metadata won't reveal anything to Google except time/date of a single message and the message size. I pointed out there may be more information there.
I have no doubt that the NSA can do traffic analysis, or may have some of this data already... I'm not sure why that is in the replies to my comments in this thread.
More worried about NSA correlating the two after getting the data from Google, but the one good thing about their centralization model probably is that with millions of users to a central server (and something you do as often as texting) this makes timing analysis extremely difficult.
But the "observer" can still know which mobile phone is yours and who communicates with whom? Especially if the "observer" has the info from the Signal servers.
Edit (as i can't post you reply to your answer):
And based on the NSA principle of the "thee levels of distance" everybody is reachable as long as some common numbers are in our contact lists which we happily upload.