Yes and no! As this is a dream, you are correct in assuming that cognition plays an important part in how the setting reacts. However, it's important to note that regardless of lucidity, no character is in complete control of what happens in the tunnels, but their influence does matter. Damien's hacking abilities will work as he becomes more lucid, but they will not always be reliable. How you choose to interpret this is up to you, but he will not be able to use his hacking to physically manipulate the tunnels or attempt to escape the underground.