By "somewhere" you mean "at the top of every Gmail page"? Then yes, I'd figure that something Google prominently displays at the top of every Gmail page is probably pretty important to them.
I mean... when something is widely displayed in the middle of a list of things that includes
* Gmail
* Google Docs
* Google Calendar
* Google Photos
* Google Search
and nothing else, then I would naively consider it to be roughly as "core" as the other things on the list. You wouldn't? Why not?
I've never thought about a definition of a "core product" before, but it seems to me that it would be something that the company takes seriously, dedicates a lot of time on, and consciously depends on for user retention and growth. I don't think Reader fit any of those descriptions, and the placement alongside actual core products was an advertisement - a hope that it might become something more, but it never did.
