No, because Mozilla don't own them, Google does.
The problem is not Google having a browser, open or closed. The problem is all the influence Google has elsewhere.
Do you mean rolling a new protocol in Chrome without warning that magically makes Google faster because they rolled it out on their end as well? This already happened with https://en.wikipedia.org/wiki/SPDY.
As long as what they do is technically good and not too heavy-handed, developers won't resist. In fact it is likely to be welcomed. But the effect will constantly leave Google a half-step ahead of everyone else on the upgrade train. After all it isn't hurting developers, it is just leaving Google with a slightly better competitive edge.
Where can users go if they still want YouTube to work well?