Such skills are certainly a bonus, but they would not be a requirement. It is common thinking that every good general should first have been a good footsoldier. The reality is that the vast majority of great generals never were. The most important skills for senior leaders to succeed are rarely similar to those needed to succeed on the front lines of any project.
Actually, was a manger in the private sector (legal) and am now in the public sector (military). I have seen both sides and have seen managers succeed and fail in both transitions.