To answer your question... no they don't. Or perhaps very, very rarely. It doesn't make sense to spend hours at a time on any of those tasks, and you can't anyway because someone always needs something from you.
When you're coding, there's a specific thing that you're trying to do that gives a certain satisfaction: there are stages of completeness that you hit (eg all the tests pass) which feel like natural checkpoints. Passing them makes you feel good. You struggle with nature, you prevail, you feel good. Before you did your thing it was broken, now it is fixed.
When you're arranging stuff for a team, the actual thing you're doing doesn't provide satisfaction in the same way. Arranging meetings, setting goals, that sort of thing is a softer level of completeness. For one, there's no real failure: the meeting will happen sooner or later, the goals are kinda obvious even though they are vague (grow revenues, make a roadmap). You can't mess this up, so you can't succeed. Yes there are reckonings when you're a manager, but they're not little ones that come every day on a timescale of a few hours.
With flow you need to feel like the thing you're doing is challenging. You need to be strong to break your PB in weightlifting. You need to be smart to fix that bug. There's nothing in powerpointing a slide deck where you are challenging yourself, it's mostly grind.