Very much so. I think your simple definition above trends toward an explanation of operational warfare. In my previous answer, I'd was trying to pull out some of the unique skills required to do what you state above.
Operational art contains many tools for conceptualizing military operations at large. That doesn't mean we are working at the operational level. Again here, an overuse of the word "operation" contributes to our collective confusion.
There are no hard or fast rules, however, I'd have a hard time being convinced that a series of company operations would end with a strategic effect. Rather, these "operations" are more likely a series of tactical actions toward stabilizing a district. This may, in turn, serve an operational objective, such as stabilizing a key province (Kandahar, for example).
Doing "Campaign Planning" is currently fashionable in U.S. brigades. This is an operational tool that helps conceptualize, frame, and link things like, security, governance, and economics. However, this doesn't mean brigades are doing operational warfare - they are just using the tools.
The size of a unit, its area of responsibility, the tools it uses to plan, etc... are not necessarily indicative of operational warfare.
They key question to ask is whether the campaign/operation being planned sets the conditions for tactical success that in turn creates a strategic effect. This is the "linking" of tactics to strategy that must be accomplished in the operational realm.
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