No, it is not. The Knights Templar were founded to protect Christian pilgrims on their way to the Holy Land and to defend the Latin Christian kingdoms that had been founded in the Middle East after the First Crusade. The Templars ultimately completely failed at the latter task after the fall of Acre in 1291, which is why they were declining by the 14th century and why Philippe IV of France found it pretty easy to have them disbanded after accusing their leaders of heresy.

The popes had no official guards of note during the Middle Ages, which is why there are so many cases of medieval popes being kidnapped or held hostage by their enemies and having to beg some secular noble to please come save them. That, indeed, is why Pope Leo III crowned Charlemagne as Roman emperor and why Pope Gregory VII was joined at the hip to Matilde of Tuscany during the Investiture Controversy.