Can emg and nerve study be normal and you still have sciatic pain from l5s1 disc protusion?

Absolutely: Sciatic can occur without weakness. Emg will be abnormal at a certain point after damage has interfered with nerve muscle connections. That means that you have objective weakness related to nerve damage. Emg's done too early (usually before 7-10 days of weakness) can be falsely normal. They should be used to sort out if there are other reasons for pain but won't help not weak.

It depends: Nerve injury will typically show up on emg. Nerve irritation, such as from compression, could have a normal EMG while still causing pain that refers down the leg