The absence of flow is what causes blood to clot. On top of that, people are continuously on strong anticoagulants (vitamin K antagonists) or heparin.

That being said, it is difficult to tell for sure and clotting would definitely occur in multiple places throughout the body as tissues and organs start to become necrotic, as would hemorrhage due to damaged blood vessels. But whether the actual pump itself would get blocked before the battery runs out, I don’t know.