Do they turn me In or do they leave me be? What sort of jurisdiction did the allies have in treatment of each others' deserters?
How do you act? Only 300 British soldiers were executed for desertion compared with 80,000+ who deserted their posts - to answer the OP it would first matter if the deserter admits deserting, or pretends to just be separated from his unit or showed "shell shock" symptoms.
some references: http://www.historylearningsite.co.uk/world_war_one_executions.htm
edit: number typo