Changing the User Agent might help to fool a HTTP server, but not the client side scripting, where every browser offers a different API. In web applications such as GMail, this is the relevant piece.

And I confirm OPs assumptions. I also feel this is a tricky way of Google to make Firefox users feel their browser of being "slow". It is basically power abuse. As Microsoft did it in the 90s.

This might not produce the results you expect, because they might be doing feature detection.

Google would nearly certainly break the site in such a way that they have plausible deniability.

Browser fingerprinting these days goes FAR beyond trivial user agent values.