How is the behavior of an amplifier dependent on $V_{CC}$?

So long as the transistor is properly DC-biased, the AC behavior of an amplifier like the ones we considered today does not depend on the specific value of $V_{CC}$. When we make the AC equivalent, $V_{CC}$ is treated as if it is at ground, so the value doesn't matter.

However, note that the value of $V_{CC}$ does matter for proper DC-biasing of the transistor. It must have a value such that the voltage through the base resistor voltage divider at the transistor base is large enough to keep the transistor ``on'' (i.e., in the linear active regime) throughout the entire input voltage swing.