No, I don't believe so. At the start of the story, I almost wondered if I had started to read the wrong book - Snow was so normal, unlike his evil self in The Hunger Games, Catching Fire and Mockingjay. From my reading, I noted that as the story progressed, Snow gradually changed to become eviler (and more of a narcissist). To answer your question, I would say half and half - he is presented in the first part of the book as an ordinary human being, and in the second half, he is presented as a narcissist. Some of these changes are present in everyday items, others in actions or feelings. I have listed some below.
Coriolanus Snow often sniffs a compact of his mother's. Some may regard this as creepy, but it proves that Snow does love his mother, even though she is dead. The compact, before entering Lucy Gray's hands, is a symbol of the past and childhood of Snow.
His mother used to sing him a song at bedtime. It had mentioned loving him. He thought of the photo in the silver frame he kept on the nightstand by his bed. His beautiful mother, held him when he was about two. They were looking at each other, laughing. Try as he might, he could never remember the moment the picture was taken, but this song crossed his brain, calling her from the depths. He could sense her presence, almost smell the delicate scent of the rose powder she wore, and feel the warm blanket of security that had enveloped him each night. Before she died. Coriolanus still kept his mother’s compact in a drawer on his nightstand. In difficult times, when he had trouble falling asleep, he would click it open and inhale the rose scent of the silken cake of powder within. It never failed to calm him with the memory of how it had felt to be loved like that. - Coriolanus Snow
When Snow swims in the lake, the powder is changed into a sort of glue that sticks several photos together. He attempts to pull them apart but tears them. In doing so, he destroys the past where he focused on love, and turns to the future where he focuses on power.
He went to the bathroom and emptied his pockets. The lake water had reduced his mother’s rose-scented powder to a nasty paste, and he threw the whole thing in the trash. The photos stuck together and shredded when he tried to separate them, so they went the way of the powder. - Coriolanus Snow
Snow's Relationship With Lucy Gray
Lucy Gray is Snow's girlfriend for most of the story. She is probably the smartest character next to Snow himself. Lucy Gray is also the only character that recognizes that Snow has changed during the time she has known him. At first, Lucy Gray and Snow have an ordinary lovers relationship, where Snow feels jealous when Lucy Gray sings about a lover that is not him. Another part is where Snow is worried about her well-being as she enters the arena. Both scenes show genuine emotion, based on the way Collins describes it.
Coriolanus knew it had hit home, this dark, moving, far too personal account of her life. He knew the gifts would pour into the arena for her. That her success, even now, reflected back on him, making it his success. Snow lands on top and all that. He knew he should be elated at this turn of events and jump up and down inside while presenting a modest, pleasing front. But what he really felt was jealousy. - Coriolanus Snow
"I don’t want to die,” she whispered. His fingers brushed the tears from her cheeks. “Of course, you don’t. And I won’t let you.” She sobbed on. “I won’t let you, Lucy Gray!" - Coriolanus Snow, Lucy Gray
This love relationship changes when Lucy Gray realizes Snow killed Sejanus. She proves this by singing "The Hanging Tree". Snow shoots at her, making an attempt to kill her.
Are you, are you
Coming to the tree?
Wear a necklace of rope, side by side with me.
Strange things did happen here
No stranger would it be
If we met up at midnight in the hanging tree.
Yes, I get it, Snow thought. You know about Sejanus. “Necklace of rope” and all that. - Lucy Gray singing, Coriolanus Snow
Dr. Gaul and Snow
Dr. Gaul is the character that Snow fears (and perhaps admires) the most at the end of the story. She is in charge of the Games and creates mutts. In one meeting with Snow and Clemensia, she uses her snakes to attack Clemencia. A few moments after Clemensia is attacked, Snow is horrified and questions whether or not Dr. Gaul even cares about human life (and what sort of monster she is).
“But I — She —” he stammered. “Will she die?”
“Anyone’s guess,” said Dr. Gaul. She had dipped a hand back into the tank and was lightly trailing her gnarled fingers over her pets. “Clearly, her scent was not on the paper. So, you wrote the proposal alone?"
Coriolanus made it down the street and around the corner before his legs gave way and he dropped onto the curb. The sun hurt his eyes, and he couldn’t seem to catch his breath. He was exhausted, having not slept the night before, but hyper with adrenaline. What had just happened? Was Clemensia dead? - Coriolanus Snow, Dr. Gaul
Eventually, Snow stops questioning Dr. Gaul at the end of the story. He even agrees with her, that the districts should be suppressed because of what he saw in District 12. At this moment, it becomes apparent that Snow considers Dr. Gaul to be a mentor and not a monster anymore.
He felt pulled right back into the old tutorial with her as if nothing had happened. “Yes, it was eye-opening. I thought about all the things we’d discussed. Chaos, control, the contract. The three C’s.”
"Did you think about the Hunger Games?” she asked. “Would you change your answer?”
Coriolanus remembered the conversation he’d had with Sejanus as they’d unpacked his duffel. “I’d elaborate on it. They’re not just to punish the districts, they’re part of the eternal war. Each one is its own battle. One we can hold in the palm of our hand, instead of waging a real war that could get out of our control.”
“And they’re a reminder of what we did to each other, what we have the potential to do again, because of who we are,” he continued.
“And who are we, did you determine?” she asked.
“Creatures who need the Capitol to survive.” - Coriolanus Snow, Dr. Gaul
I have chosen three areas in which great change occurs. There is more change in The Ballad of Songbirds and Snakes when it comes to Snow. The possibilities are very wide. The change in Snow causes him to slowly become a narcissist, but the vast majority of the blame should be put upon environmental and human influences.