otherwise it would show at least a little bit of its night side.
I'm going to guess you've more of a background in mathematics than science. As the old joke goes:
A mathematician is walking over a field. Suddenly he hears a voice over his head. "Hey, you there! Where am I?"
The mathematician is confused and looks up to find a hot air balloon, hovering above his head. The voice shouts again: "Yes, I meant you. I have lost track due to the fog. Can you tell me where I am?"
The mathematician thinks for a moment, then looks up again and answers: "Ah, I know! You are in a hot air balloon!"
The man in the balloon answers: "Thank you, but you're a mathematician, aren't you?"
"How did you know that?"
"Well, your answer was perfectly correct and absolutely useless."
Yes, it will
technically show a little bit of a night side, but with the relative size of Mercury and the Sun, that little bit is just not going to be meaningful or noticeable to the human eye.