Yes and no. The Jesuit order (ie, the Society of Jesus) was one of the foremost Roman Catholic forces in their Counter-Reformation effort, led by the Jesuit founder Ignatius of Loyola, who was certainly a staunch opponent of the Protestant Reformation. The Jesuit missions of Catholic education and missionary work, along with their oath of total obedience to the Pope, certainly played into that as well.

However, the Society of Jesus was first authorized by the Pope in 1540, five years before the beginning of the Council of Trent (the cornerstone of the Roman Catholic anti-Protestant response), and they were well established and influential by the time Trent concluded in 1563. It's likely that the Protestants were significantly in Ignatius' mind when he wrote that the Jesuit order's goal was the "defense and propagation of the faith", but while suppressing Protestantism was a part of that, their aim was broader than simply being anti-Protestant.

Would the Jesuits have been established if the Protestant Reformation had taken place? Certainly Luther and the later Reformers helped created a climate in the Western Church and called to the forefront certain issues in the Roman church that required a response. But there was already a strong undercurrent of reform within the Catholic church led by humanists like Erasmus that had little in common with Luther et al. It seems plausible that a similar type of order would have come about with the renewed focus on personal devotion and piety and the rejection of worldliness and corruption in the church hierarchy that was present even apart from the Protestant movement, though perhaps it would have looked different (the emphasis on unswerving devotion to the Pope would have been less critical in a scenario without Protestant separation from the papacy).

TL;DR: the Jesuits were a crucial part of the Roman Catholic Church's Counter-Reformation efforts, but it's not quite accurate to say they were established as a response to the Protestants.