To share my perspective, outside Google:
A similar "error/ad" appears for other some other Google features. Such as trying to edit a picture in Google+ -- I've seen that example for so long now, it seems there's no intent ever to change it.
With each such example, the cumulative effect is to remind me of bad days in the past. My feeling isn't snarky, it's unease. I've seen stuff like Prodigy and CompuServe. I saw Microsoft pivot MSN 1.0 from being another such service, to instead be a web site.
And ever since, I've seen a succession of attempts to "put the open internet genie back in the bottle", including but not limited to Internet Explorer. So far these attempts have failed... but they haven't been from a company as powerful as Google.
So as someone who had loved Google for many years as a supporter of the open internet, it makes me unhappy and confused to see more examples of "Download Chrome!" as an error message in Firefox.
Having said all that, I'm happy to hear that you plan to address this at least for Inbox on Firefox.