Can I claim to have completed my degree on my résumé, prior to convocating and receiving the physical diploma?
You can use the formulation 


  Degree to be conferred MM/YYYY


to indicate that you have passed all degree requirements, but are waiting for the degree to be officially awarded. This occurs fairly frequently, particularly for PhD students, who may finish at any time of the year, especially if their university only confers degrees once per year.