If Google is there, they would. And if not Berlin is one of the few cities on this planet where people actually live in the city center and drive outside for work.

IBM has a train station outside of the city in Scotland, why couldn't Google do that?

People already do for things like university and other companies around the airports. It would be an experiment for Google of course, but they have the means and it could change public opinion massively.

I worked in Charité in Wedding - it was fine, the only pain was I was living in Schlachtensee so I had a huge commute every day.