Ok, I never went in that direction with the story, but with the two of them hanging out together (pun intended) and nothing else to do, no doubt they would have talked with each other. However, bear in mind that he was crucified the day before and might not have been completely lucid by that time.
We have a record in the Bible of Jesus and the two thieves crucified on either side of him talking with each other, and somewhere, which I cannot find at the moment, is an account where testimony of a crucified man was considered legal. So there is some evidence for the idea that those dying on the cross could and would converse with each other and with those around them while suffering. I say this because I have tried to keep this story in the realm of fiction rather than fantasy - that is, while this episode did not happen, it was possible, both physically and based on Roman culture of the time.
Now, would Sabina have revealed her true identity to Regulus? The short answer is NO.
Why? She is suffering from something we would call Dissociative Identity Disorder, what we used to call multiple personalities. In her alternate personality, created by her overwhelming obsession with crucifixion and her role-play as a slave, her alternate personality was reinforced and became stronger until it could dominate.
How did that happen?
Going back to her life in Pompeii, when she was into crucifixion play in a brothel, she role-played as a slave girl, swapping identities with her actual slave, who whipped her and tied her to a cross. When she was able to turn over control and become a slave (in role-play) it didn't take many times until she could fall into her role completely. In the last chapter, Julia Lepida (the real Sabina) says it was hard to bring her back to reality to escape even when Vesuvius was erupting and ash was raining down on Pompeii:
I hurried back and got her down from the cross, trying to shake her out of her role as a disobedient slave long enough to get her dressed and moving. She was angry and fought me all the way out to the street, where the shock of what she saw finally brought her back to reality.
Also, after they escaped:
The ship took us north across the bay to Misenum where we joined hundreds of other refugees, looking for our lost families or any familiar face. But they were gone, all of them, buried with the city under tons of ash. We were alone.
She escaped from the reality of her loss by retreating completely into her fantasy role. I had no choice but to adopt the role of domina, terrified of what would happen if anyone found out.
Now, she has been Sabina the slave girl for about two months with the only break being when Julia Lepida (the real Sabina) argued with her until she finally punched her in the eye and gave her an ultimatum - crucify me or be crucified yourself. She immediately resumed her role, and her domina says:
As quickly as she had appeared, the real Julia Lepida was gone forever. I never saw her again, not even during the days of agony of the cross. When she begged for mercy, begged me to stop, she always addressed me as Domina, never Sabina. And I knew that no matter how desperate she sounded, she was playing her role to its end, and my life depended on me playing mine as well. Even though my heart was breaking, I didn’t dare to stop what was happening.
She had an obsession which she fed and fed but was never able to satisfy. It kept her awake at night, it drove her to go watch others be crucified, she played at it when she could contrive to arrange it. It overwhelmed her and she became absolutely convinced her only escape from it was death. She could have used poison, slashed her wrists, etc. But this was also her opportunity to experience what she could only dream about, and she took it.
She wanted Julia Lepida (the real Sabina) to have her crucified, but she argued, tried to reason with her instead. When Sabina (the real Julia Lepida) punched her in the eye, she set events in motion that she could not control, neither could she escape. (Nor could Julia Lepida/Sabina) Having triggered the process that would end with her death on the cross, she could abandon whatever vestige of her true identity might still have remained. From that point on, others were going to take her and punish her as Roman law demanded.
Finally, bottom line, she would not reveal her true identity to anyone else because for her,
that identity no longer existed.