Germany has been very good to Spec. André L. Shepherd since he deserted the U.S. Army. The 31-year-old former mechanic of the 601st Aviation Support Battalion is enjoying perks that eluded him back home in Ohio: a bed, a bank account, a cellphone and friends. Best of all from his standpoint, he isn't back in Iraq. "I'm having the time of my life," says Mr. Shepherd, the only American bunking at a refugee-processing center in southern Germany. The U.S. deserter enters uncharted legal territory on Wednesday, when Germany begins weighing his request for political asylum. The case will put to...