I spend 10-20% of my time at Google (depending on the needs) developing and maintaining an internal tool that is used by 100-1000 engineers across 10-100 teams (not including my current team). Not only have my last 3 managers been extremely supportive of this, I've netted a few peer bonuses from this, and some nice feedback from senior people that appreciated my work.
The "approval from my manager" amounted to telling them in our weekly 1:1 meeting that I wanted to spend my 20% time on that project.
Of course, if you spend 20% of your time working alone on something that produces 0 results in the span of several quarters, I suspect your experience is not going to be the same.
You've made yourself an integral part of the company and gotten your name out there to boot.
Back when I worked at Compaq there was a tool everyone used in the build process and it had a splash screen that mentioned the author. That guy was a legend at Compaq because everyone had at least heard of him. When my buddy took over the build process he ended up emulating Mr. Legend and put his name on his tool that was used thousands of times a day. Same thing happened to him: oh you're the Mr. Coder? He had his pick of projects for a very long time.
The "approval from my manager" amounted to telling them in our weekly 1:1 meeting that I wanted to spend my 20% time on that project.
Of course, if you spend 20% of your time working alone on something that produces 0 results in the span of several quarters, I suspect your experience is not going to be the same.