It should not. Being a doctoral student is typically a full time job. The only exceptions I know of are industrial PhD students in technology subjects who are doing their studies as part of their employment at some company in collaboration with the university and students in different medical subjects, such as medical physics, who are working part time with clinical duties and part time with their PhD. Also keep in mind that even in those cases, a part time PhD can take on the order of 10 years to complete.