The practice of devshirme was the way the Ottomans built their armies by recruiting young children from Christian families and educating them to be loyal only to the Sultan?

Yes. However, The process of Devşirme was much more insidious than just a system that "recruited" young children to serve the Sultan.

Devşirme robbed innocent Christian citizens of their children in the Balkans. The parents would have no choice as to whether their children would be deprived from them. It was a tax. They would be brought to the Sultan in Istanbul and forcibly converted to Islam at the tender age of five years. The women would grow up to be part of the Sultan's harem. While they served the Sultan, each woman could hope that her son would be chosen as the Crown Prince and she could have court rights, but she could never hope to have rights to her own body. The men were educated in the arts of war and diplomacy. The ones of who were more physically capable would become the feared shock-troops of the Ottoman Empire: the Janissaries. Those more skilled in diplomacy would be the ministers of the Sultan's court.

Devşirme Story

A devşirme story that Turks like to tell was of the theft of a child from a Serbian noble family. His older brother (by two years) remained with his family. The younger brother did not know he had an older brother and only discovered this by accident. The Serbian noble who remained in Serbia became a Patriarch of the Orthodox Church. The abducted brother became the Governor of Serbia. The first time that they met, they did not even recognize each other (since they were now in their late twenties and they had never met since they were 5 & 7). But they were forced to work together and they realized how similar they were. The Governor realized that he was the brother of the Orthodox Patriarch and the two men embraced. (One wonders how many abducted children would never find their families again, especially the women who could never leave Topkapı Palace.)