Validate that a threaded binary tree works as intended
Shortly - no, it is not safe.
Huge random test does not guarantee success (but of course, when there is a bug, it finds it in the most cases).
To test threaded tree with deletion and insertion you need to have saturated all nodes (with thread links), make them change thread, the same for deletion.
To make sure it works all corner cases must be covered both for insertion and deletion. With huge input there is huge probability it works, but this is not conclusive. Also making more passes (more test) it increases probability of success, but nothing more.

To test it manually - case by case - you do not need very big tree (I did tests on double threaded AVL, tree height was maximally 5).