I don't remember Google (search, at least) ever not working in any browser I tried, and I used some oddball browsers over the years. Maybe apps like gmail and docs, but they simply would not work in other browsers. Remember in its early years Chrome was a darling because it was supporting the "modern" web. That was the whole stated reason Google developed Chrome: to support modern, rich web applications, and force other browsers to do the same if they wanted to stay relevant. Nobody guessed that Chrome would eventually be the new IE.
Google has a very long history of downgrading or even outright blocking off their services based on User-Agent. Them doing it to Opera in particular was a big story back in those "early days". And no, it's not because it wouldn't work - people literally made it work by spoofing the UA.