Not OP, and nothing makes it impossible, but from my experience in big companies, being visible is way more useful than being productive.

I got further faster by just answering emails right away than by churning out code. I got constant kudos, which got me promoted, and invited to more meetings, which led to less actual work. All because I just started replying to emails sent to our group. In retrospect it feels pretty perverse.

In lean companies and startups...perhaps not so much.