Is it possible to churn butter in a food processor or blender?
Sure, why not? It probably won't turn out quite like the stuff you get at the store, but all you need is cream, a way to churn air into it, and enough agitation that the milk fat molecules start to clump together.

It will require some manual work once you've got the butter and buttercream separated. But the food processor will get you most of the way there without too much of an arm workout.

Check out this PBS article on DIY butter with a food processor.