Compability of Brew Cask VirtualBox and Parallels?
Yes, the brew cask virtualbox and Parallels Desktop 12 seem to be compatible. I tested them and they are working together.



Anyway if they become incompatible at some point, there are also other alternatives. As mentioned in the comments, other alternatives contain 


Parallels Desktop 12 for Mac Pro Edition where you can use the free vagrant-parallels
also an experimental vagrant provider for xhyve > shave > Apple > Hypervisor.framework by this comment