It won't have any effect (assuming it's wired properly, etc.).
The input impedance of the MSGEQ7 is 1 Megohm which is high-enough to have no effect on a line level or headphone-level signal.
It IS possible to get noise back-into the audio circuits through the ground or power supply when the lights switch on & off but I wouldn't expect that.
BTW - The MSGEQ7 is a [u]spectrum analyzer[/u] chip. It's mis-named as a "Graphic Equalizer" although it may have been designed to be used as a display built-into an equalizer.
...The Arduino has even higher input impedance ...as long as the input is positive. If you feed an AC audio signal the internal protection diodes can clip (distort) the negative half of the signal (or worse). When the diode "kicks-in", the impedance drops to very low, essentially shorting-out the audio. But, the MSGEQ7 is designed for AC audio signals.