No more than I would call a corner store a restaurant.
I can see what you mean, but I think looking at the role of a cook as only preparing food might be too narrow a view. A proper cook has to know where they're getting their ingredients from, at what price, and how the hell they're going to be turned into food, and how long this will all take; long before a single knife is taken in hand or fire is kindled beneath a pot. Scaled to large spans of time or numbers of bellies, this becomes a task of organization and planning much like that of planning a military campaign. Which should hardly be surprising, given that an army marches on its stomach.
In the modern context for example, a high end restaurant's head chef will know what's in season, where they can source it from, at what price, and will design their menu for that week
only when they know these things. They'll then run that through with their section chefs and other immediate subordinates (that number will vary depending on the size of restaurant and how classically structured it is), who will actually take charge of the cooking. The head chef will spend their time pacing the kitchen supervising (though in a well running kitchen, they shouldn't need to do too much of this)*, badgering suppliers over the phone, redesigning the menu, and designing new recipes. I make this digression only in an attempt to impress on you just
how much of being a cook isn't actually about cookery, as counter-intuitive as that may be.
I haven't got my Landsknechts book on this laptop, but from what I recall, the
sudler owned a bunch of ladles, minded the stockpots, and sourced stuff to go in them, right? They were essentially a quartermaster specifically tasked with food (broth, more specifically), which is what any cook actually managing a kitchen has to be. So even though they didn't actually cook meals for people, I think there's a valid sense in which you can call them at least similar to a
head cook, because of the multiplicity of logistical roles that are heavily associated with stocking and managing a kitchen in the real world. I probably should have said so in my first post...
Meandering back to the point...
@Sucal was asking this for the purposes of making an RPG character, right? I think a big burly fellow who carries a cast iron pot on his back, has a brace of ladels at his waist, and knows where the onions will be in any village he walks into strikes a pretty dashing (if unconventionally so) image.