Short answer. Yes, maybe. I guess it can work without if one watches out.
Yet, I see the leader as the person who picks up whatever would fall through the cracks, and in my experience, no circle structure/set of aims/domains is ever tight enough so nothing falls through the cracks. So I’m not worried about the aims/domains of the department circles but those things that lie between them or aren’t covered by the department circle aims/domains yet. By the way, no one says that this operational leader has to be an extra person, it can simply be one of the leaders/delegates.
In my community, for example, for years, there was not leader of the GC, and then the GC itself begged to have one because they noticed that the leaders’ + delegates’ energy was in the department circles and not in the overall overview. They explicitly wanted someone as the 9th person, not for one of the 8 to play that additional role.
So if you go ahead without a GC leader, keep your eyes open to see if you notice the same dynamic, or any dynamic that suggests that a leader would be good to have.
From this I assume you’re also not planning to have a Mission Circle. And my answer there is the same: in the beginning, people often don’t want it and then they add it later. Which can be easy, or it can become its own power struggle. So having it from the get-go might, in hindsight, be the best option; but I understand if its not in the cards.