SVReg definitely makes use of available cores. So for surface registration, it processes 2 cortical hemispheres on 2 separate threads. During volume registration, whenever possible, it processes 3 coordinates on 3 threads.
Moreover, each of the separate threads use multiple CPUs during various operations such as conjugate gradient minimization and interpolations.
So yes, the more cores, the better it is for SVReg processing.
Additionally, you can also process multiple subjects simultaneously if you have computing power.
The system you mention is definitely great (both).