Usopp will awaken Conqueror's Haki. It's befitting for him to do so upon finally becoming a Brave Warrior of the Sea.
People don't seem to realize, but Usopp has one of the highest willpowers in the entire series. I know it might sound crazy, but allow me to elaborate.
Usopp is considered as close to a normal human as possible by One Piece's standards, and is also one of the biggest cowards any series has ever seen. Yet the guy consistently pushes through his cowardice to stand up to superhumans, and enemies far beyond his capabilities. This isn't just a simple matter of pushing through your fear. Every time Usopp does it, he is literally putting his life on the line to do so, and he knows it.
This might seem inconsequential at first because of how many people stand up to those who are stronger than them, but in comparison to Usopp, those people aren't deathly terrified when doing it. Usopp is, and in turn, he has to overcome an immense emotional roadblock every time he's put into these type of situations. It takes an insane amount of willpower for a Normal human to break through their fear, and stand up to a superhuman. \
This isn't even to mention the sheer amount of damage that Usopp can withstand, and pushes through despite being a "Normal Human." Things that would easily kill someone of his likeness, 1000 times over, but he survives on sheer willpower alone.
When Usopp finally sheds his cowardice for good and becomes a Brave Warrior of the Sea, he's still going to have this immense reservoir of willpower at his disposal. But it will no longer be focused towards him not being a coward, and that's when his Conqueror's Haki will bloom.
