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.
Did anyone say they couldn't?
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.
Form a straight question and you'll get a straight answer.
I'm beginning to suspect the answer is "nothing", and that this whole thread is really just a superstitious allergy to GCM.
And even though your question is off-topic, I already answered it above.
Why would you accuse someone of being allergic to a technology when they are simply answering questions about it? If you disagree with the actual topic of discussion - that Google (not the NSA) might get more than just "message sizes and timestamps" out of an E2E-encrypted app which uses GCM messages - then have a normal conversation about it instead of bringing up the NSA repeatedly.
And if not, then stop making baseless and inflammatory accusations.
The parent poster of the post you initially replied to asserted that Signal was "giving NSA the only thing what they want: metadata from Google", so I guess that's where tptacek is coming from.
On a side note, Google can't actually know the message sizes because GCM is used without a payload.
Your side note also applies to that comment, but not mine, so I think it belongs there, not here.
Google knows device A got messages at times X, Y, and Z, and device B got messages at times X+1, Y+2, and Z+1.5.
I'd be willing to bet with some statistical analysis over time, some pretty interesting data could be mined from that raw knowledge.