The Star Wars prequel trilogy would have been vastly different had Qui-Gon Jinn survived the Duel of the Fates, begging whether the Jedi in question would have served in the Clone Wars. While Qui-Gon's hypothetical survival could lead to the argument that the Clone Wars could have been avoided due to the connection he would have had with Anakin, the methods of Darth Sidious/Emperor Palpatine are enough to render this void. As shown in the Star Wars franchise countless times, Palpatine has the genius to twist any situation to his advantage, with numerous contingencies in place for any possible change in his plan.This leads to the conclusion that the Clone Wars would still have happened should Qui-Gon have survived his duel with Maul and the events of Star Wars: Episode I - The Phantom Menace. In this case, the question turns to whether he would have served in the galaxy-altering war that followed. There is no denying that a lot of Jedi did not agree with their involvement in the war, nor the actions committed by either side throughout its three-year period. With Qui-Gon's motivations being driven by something very different from the Jedi Order's - in ways the Clone Wars would have directly affected - the question makes for compelling arguments.
Qui-Gon Jinn Would Have Been Cut Off From The Force's Guidance
While Qui-Gon Jinn was a revered member of the Jedi Order, often sought out for his counsel, wisdom, and the respect he had garnered in his life, he was also considered somewhat of a maverick. The reason for this stems from Qui-Gon's adherence to the will of the Living Force. Due to this, Qui-Gon - most recently shown in Obi-Wan Kenobi - tended to follow the will of the Force regardless of whether this aligned with the wishes of the Jedi Order. This, therefore, leads to the exploration of whether Qui-Gon would have fought in the Clone Wars.
These two aspects link due to the Clone Wars' effect on the Force, and more importantly, the Jedi's connection to it. Given the dark state of the galaxy and Darth Sidious's manipulation of events, the dark side of the Force began to cloud the Jedi and their judgment. Considering Qui-Gon Jinn has an even stronger drive to carry out the will of the Force, this weakened connection would likely mean he had no choice but to follow the will of Yoda and the Jedi Council among his peers
Qui-Gon Would Likely Have Initially Served In The Clone Wars
Due to this lack of connection to the Force, it is safe to assume that Qui-Gon Jinn would have served in the Clone Wars. With the likes of Mace Windu and Yoda insistent on fighting the Clone Wars - despite the latter disagreeing with the principle, as revealed in the Star Wars: The Clone Wars episode "Sacrifice" - Qui-Gon's clouded motivations would likely have caused him to do the same. At the start of the Clone Wars, the fight seemed morally right due to the Jedi's obligation to protect the people of the galaxy and stop Dooku, a former Jedi, from threatening the peace they fought for.
Also, stemming from this, Dooku was Qui-Gon's old Jedi Master. This could have caused Qui-Gon to feel even more inclined to fight in the war, potentially as a way of reaching his former mentor after discovering Dooku's fall to the dark side. All of this supports why Qui-Gon could have served in the war at first, yet also leads to the conversation of whether the Jedi would have eventually abandoned the Order.
Would Qui-Gon Have Abandoned The Jedi Order?
One of the more compelling elements of Star Wars: The Clone Wars was its exploration of the Jedi becoming increasingly jaded by the titular conflict, especially through the story of Ahsoka Tano. After the arc in which she lost faith in the Jedi Order and her increasingly differing views on the role of a Jedi itself, Ahsoka left the Order to become more of what the Jedi should be, rather than what they were in the prequels. It is safe to assume that Qui-Gon Jinn would have followed this path also.
Despite the dark side of the Force shrouding the Jedi, someone as devout to the ways of the Force as Qui-Gon Jinn would have eventually sought to once again strengthen the connection. In doing so, Qui-Gon likely would have done a lot of soul-searching, eventually realizing that fighting the Clone Wars may not have been the best move by the Jedi Order. This would likely have resulted in Qui-Gon realizing the will of the Force was for the Jedi to abandon the war, leading him to subsequently abandon the Jedi Order as a result, in what would be a vastly different version of the Star Wars prequel trilogy.