Is it safe to shallow fry frozen burgers without defrosting them?

No. There are food safety concerns associated with partially cooking frozen burgers. While the outside may cook thoroughly, the center isn’t likely to reach the proper safe-cooking temperature. Any harmful bacteria that may have been on the frozen burger might not be destroyed. You can tell when a burger is completely cooked when the color changes to opaque throughout, with a slight hint of pink in the middle at the most.