most likely the voltage will fluctuate because some other component in your cd player needs current. because there is no such thing as a perfect power supply, voltage will unavoidably drop if some components need instantly a high current.
local voltage changes don't occur that often (only if you move from an area with 220v to 230v or so), and because they are after the regulated power supply in your circuit, they mostly do not matter that much.
and long time voltage changes do not really matter either, as long as the voltage is above the minimum working voltage the opamps/dacs/etc in your player. as said above, the power supply filters and regulates down the voltage to a much lower voltage anyway
the problem are the very short time voltage fluctuations (from local components, as said above).
imagine this: the DAC chip needs a stable reference voltage, often 5V. it then routes this through a resistor network which operates as a voltage divider. this is how the analog sound is generated. now, if say for example the voltage isn't exactly 5v, but fluctuates around 4.99 and 5.01v. this also means that the output of the dac will fluctuate too - this is to say the volume. roughly saying, voltage equals volume. so with a fluctuating voltage in your cd player, volume will also fluctuate. and you may know the effect of fast-fluctuating volume by the name "noise"
oh and it's the same too with for example the opamps: fluctuating input voltage, fluctuating output voltage, and voltage equals volume.
so no pitch change, mostly noise.