Yes. Brand helps recruiters understand a role quickly, but strong operating responsibility can be compelling even at a small company.
The key is making the scope legible. The leadership experience in consulting applications guide is useful for showing ownership rather than just listing duties.
Quantify what you managed and changed: revenue or cost impact, team size, process improvements, growth, decisions owned, or difficult problems solved.
Also be realistic about level. Strong small-business experience may create an interesting profile, but the firm will still evaluate how that scope maps to its own role expectations.