Would Moore have commanded the coalition army?

If Sir John Moore had brought two-thirds of the available troops, would he have become the de facto overall commander?

Probably: a 10,000-man British force with infantry, cavalry, artillery, and its own logistics would have outweighed the roughly 5,000 Swedish troops in the field.

Moore's hypothetical contingent would have provided about 10,000 troops alongside roughly 5,000 Swedes. It would also have brought riflemen, cavalry, artillery, and its own logistics train. His larger, self-contained force would have made him the practical overall commander, with the Swedish troops forming a division within the combined army.