The Order of Brothers of the German House of Saint Mary in Jerusalem, the full name of what is commonly the called The Teutonic Knights, like almost all of the crusader knights orders it was set up to aid those on their travels to the holy land, making great profit for the members of the order.
Becoming wealthy and powerful its leader was asked by the pope to assist in purging heresy from Poland and the east of Europe, with terrifying results.
in answer to your question, yes they were involved in the crusades, acting as mercenaries and as holy warriors, the same as nearly every single knightly order in Europe was involved.
