Yes, but once you're "the guy/gal who wrote $SUCCESSFUL_GOOGLE_PRODUCT", you have a lot of credibility, experience, etc. as resources to make your own product that you do own.

The point of the 20% products for Google is to give the company startup-style flexibility. It works the other way, too - if you take a product from whiteboard doodling all the way to an official Google product, well, a startup is like that, except 100% of the time, on your own bank account, and with no admins/middle managers to take care of the business side for you.

I'd guess ex-Googler startups tend to draw more from their founders' general experience at Google than from specific products, but I've heard of rebooting the idea of a 20% project outside with a broader scope.