Depending on where the Coil Whine originates. Coil Whine is a Hardware problem with High powered computer components like the PSU or GPU.
If it is the GPU, Coil Whine most likely will occur when the GPU is under heavy load. So, unless Freesync causes the GPU a heavy load, it will probably cause Coil Whine.
This website gives a good explanation of Coil Whine: What Is Coil Whine, and Can I Get Rid of It on My PC?
Possible fixes to Coil Whine from link above. Need to go to link to find out the possible fixes. Copied from link:
What Can I Do About It?
Sadly, there isn’t an easy fix for coil whine, like an updated driver or a Windows setting. It’s a physical property of your graphics card (or any other component you can hear exhibiting the noise). The fixes for the problem, therefore, are going to be physical in nature. You have a few options.