Doubt it will succeed. I use "hoover" when I'm actually using a Dyson. I'd never say I'm googling something when I'm actually using Bing.
Your expectations make it sound like you've only worked at companies with terribly unhealthy workplace cultures. When I joined Google, I remember noticing that probably 50%+ of my coworkers used iPhones. That changed with all the free phones they gave out, but any place that would "culturally oust" you for not drinking the Kool-Aid sounds like a nightmare to work at.
I don't know anyone who literally means "Google" when they say to google something, though. They just generally mean search.