They could probably exist without Google funding, like just supporting a Chromium fork with fast native adblocking. But obviously not as a thousand people company.
It's the perfect way to kill one, actually.
1) Give them $0.2 billion a year in easy money
2) Their projects expand as per Parkinson's law so they spend $0.2 billion a year
3) Since they have easy money, they won't bother seeking alternative funding sources
4) They now find themselves in the same position as a crack whore vis-a-vis her pimp
Mozilla wouldn't ever abandon their fun pet projects, but with sufficient coercion they might abandon privacy for "fighting hate" or similar.