Looking at Ace's fights in the main story, I don't think we ever see him consciously use Conqueror's Haki in a direct offensive way like Luffy or Kaido do. He definitely has it—the vivre card info confirmed he's a conqueror. But his battles in the manga and anime, against Blackbeard and Akainu, rely overwhelmingly on his Devil Fruit power and physical brawling.
That said, the potential is fascinating to consider. He had the willpower and charisma to lead the Spade Pirates and become a Whitebeard commander. If he'd lived longer, maybe he'd have learned to coat his attacks with it, turning his 'Hiken' fist into something even more devastating. His battle style was always so aggressive and fiery, it feels like a missed opportunity we never saw those two aspects of his power combine on panel.
Ultimately, his story was cut short, so 'effective use' in battle remains a big 'what if.' It fits his character, though—his strength was more about the raw, burning passion he inspired in others than a refined, domineering force.