If you can remove the coffee grounds/filter and replace just those, then yes it will be safe from a health perspective. The plastic in the filter "cone" should be food safe, though durability may be an eventual concern. The plastic cup base can definitely be reused, as is intended.
As far as the practicality concerns go, it may be more of a pain than it's worth. The coffee containing part of the filter funnel is going to be pretty well attached, in order to keep it from slipping into the cup below and steeping (like tea) vs. simply having the water run through it. You could probably remove the coffee filter and perch a coffee pod in it's place, but it would not be sealed to the plastic cone, and hot water may run around it without actually percolating through the coffee grounds in the pod.