If you're at a giant company, the answer is likely no, there's enough politicing and paperwork where the highest impact thing to be done by a manager is likely not coding.
If you're at a startup / smaller more nimble org in a big company, the answer is likely yes, if you've gotten to the point where you're a manager, in theory you're a very good engineer and you should spend your time coding, but on things that aren't on critical path. Bug backlog, experimental things with no hard deadlines, proof of concepts, all of these are valuable things. Leading from the front is also just generally good with smaller groups.
Also under discussed by people having these debates (typically managers), is not acknowledging how bad most managers are at coding, especially if their job hasn't required them to code in a while. I see all the time that managers look for any excuse not to code, because it would reveal to their team that they're at best an L4 level coder after being in management for 5-10 years.