Can a stroke happen due to a hole in the heart?

Yes. In what's called an Atrial Septal Defect, a clot, such as a deep vein thrombosis (DVT) can travel up the inferior vena cava from the legs, into the right atrium, get shunted through the hole into the left atrium, into the left ventricle and out into circulation where it would travel up the carotids into the brain causing stroke.