Cognitive copies are still able to act and react, as long as the palace lord sees them properly. For instance, in 5R, cognitive Haru can't do anything because Kunikazu only saw her as a mindless and obedient puppet. However, Sae saw Joker exactly how he was. She heard his whole story and believed him. She saw him as a guy who was unjustly accused and had to fight to really live, which is something she resonates with. She saw the person behind the mask, which is why he appeared in her cognition as himself and not Joker. She saw him as a prisoner, which is why he appeared in the prison in her cognition. She saw him as a living, breathing, human, which is why he could bleed and die, unlike, say, the people in Kaneshiro's palace, who weren't people at all and didn't die; they just stopped being helpful.
That's why Joker getting her to believe his story during the interrogation was so incredibly important to their plan. He needed Sae to see him as exactly who he was, or his cognitive copy wouldn't be able to fool Goro. If he'd been a shadow, or perceived improperly, then yes, he would have just disintegrated when he was shot and Gor would've known. However, the interrogation let his cognitive copy perfectly match his real self.