Question: is the sole survivor a synth?
Answer: No, the Sole Survivor is not a synth. He is the “Sole Survivor”. That label in itself tells you that Nate/Nora is human, being the only fully human (Ghouls being 'evolved' or 'transmuted' humans) left in the world. Replacing the SS with a synth has no purpose, with no benefit to the Institute.