Sometimes, but with rules. Some policies allow personal holidays or side trips during the insured period, but they may impose duration limits and still exclude time spent in the insured person’s home country.
Students often assume any travel during the policy dates is the same trip. The documents usually draw a distinction between the main academic trip and personal travel taken during that period.
So the right answer is not simply yes or no. It is yes, sometimes, but only within the limits stated in the policy.