Absolutely. Of all the companies I've worked with, the one with absolutely the most effective management was the one where every manager was also a part-time IC. The head of mechanical engineering had to design a product while managing the team. The shop manager was also working as a machinist for most of their shift, or working on jig design and metrology. The head of accounting, of course, spent most of their time accounting, and only part of it managing the accountants. The head of software also wrote software, although not as much as their subordinates, and they were reviewing the codebase all the time. Of course none of the managers would chew through their IC work as quickly as people who could devote all their hours to it, so they mainly picked up tasks that weren't critical-path to avoid becoming blockers to their team.
The CEO rotated through positions, spending several months working in customer service, inventory, accounting, and even working directly on the production line. He mainly put himself on whichever team was most short-handed, although it was more to learn firsthand what their challenges were, and how the company could allocate resources to solve them. Fortunately he was a multitalented guy who could pick up those roles productively, and also humble and down-to-earth enough to not intimidate his colleagues too much when he took over the neighboring desk.
The CEO rotated through positions, spending several months working in customer service, inventory, accounting, and even working directly on the production line. He mainly put himself on whichever team was most short-handed, although it was more to learn firsthand what their challenges were, and how the company could allocate resources to solve them. Fortunately he was a multitalented guy who could pick up those roles productively, and also humble and down-to-earth enough to not intimidate his colleagues too much when he took over the neighboring desk.