The Qin army that fought at Julu would not have been the exact same army as the one that had conquered the last of the Warring States- fourteen years had passed between the last battle of the wars of unification and the Battle of Julu. A number of other campaigns had been fought in the meantime as Qin expanded north and south, and according to the narrative in The Records of the Grand Historian the Qin army at Julu had been newly raised to put down the rebellion, after rebel commanders had defeated and scattered the Qin forces originally present in the area. And in any case, over the course of 14 years one cohort of soldiers would have aged out of military service while a new cohort came of age.

That being said, in terms of organization, structure and recruitment it was very much the same army, and there is a very real possibility that a number of veterans of the earlier wars fought at Julu, whether in the Qin army or on the side of the rebels. We don't have the sources to identify any of the individual soldiers in either the Battle of Julu or the earlier wars of unification, so there's no way to identify a specific example- but given the nature of Qin military conscription it's almost certain that there were many who had fought in the wars of unification as young men who took the field again during the rebellions.

The Qin army rested on a system of mass conscription, in which every able-bodied male from the ages of 17 to 60 was required to serve at least one term of continuous full-time duty in the standing army, where they would receive some training, and afterwards could be mobilized as needed to support Qin's campaigns. This system allowed Qin to keep a relatively small but well-equipped standing army staffed by each year's batch of full-timers, to give at least some military training to a wide swathe of the population, and to quickly raise very large conscript armies from the general population when needed. It also meant that the individual Qin trooper may well have been mobilized several times over the course of decades. The other Warring States had practiced similar systems and also mobilized a large section of their adult male populations.

Given that a 17-year-old who served in the last campaigns of the wars of unification would have been only 31 or 32 by the time of Julu, a large portion of those who had been eligible for conscription in the earlier wars would still be well within military age at the time of the rebellion and could potentially have been mobilized again by one army or another. And this would be true not only of Qin veterans, but also veterans of the former kingdoms. With hundreds of thousands mobilized by the various states during the wars of unification, and hundreds of thousands mobilized again by the imperial and rebel armies, there was a very real chance of significant overlap between the two groups.