Yes, and the common definition of “productive” needs broadening to include non-profit and charitable work, for example.I had a friend that retired most of a year before me who told me, in retrospect, that he made a mistake by diving straight into a new project volunteering ~1/2 time at a non-profit that is important to him. That he should have taken a few months off to enjoy it.
I took that to heart and am right at 6 months now since I retired. And I'd recommend that sort of a break from any sort of serious recurring time commitment. I'll be starting up a ~1/2 time gig at a non-profit next week and I know that I'm awfully glad that I've taken this time off. I was never worried about being bored - what has been interesting to me is just how quickly being retired feels like my natural state of existence, and it was that full time job thing that was unnatural. In reality I think its the reverse - society needs enough people doing productive stuff right now to function, but I'm ok not being one of the people that is being productive