If you start at Google at a lower level (SWE 2 or SWE 3) your manager can unilaterally shut you down. If you get a bad "calibration score", which is set quarterly by the manager, peer feedback won't matter. No other team will want you, and you may face a PIP, which ends your career even if it doesn't get you fired.
Thus, your manager decides if you have 20% time or not.
There are good managers at Google who value 20% time and will encourage you to work cross-hierarchically with other teams or on personal side projects, and there are others who are absentee so you can pull that off furtively. If you get a hard-ass with a lot of project-specific ambition, you're not going to get away with 20% time.
Google inadvertently makes it worse by conflating project leadership with people management, which means that your boss is also held responsible for the performance of a specific project. That creates a huge conflict of interest, because the employee might be a better fit for another project, but the manager has to eat a loss on the project where he is.