Hi John,
The graphics card is primarily used for rendering. Unfortunately, ITK, the parent library, did not get very far in implementation of GPU-based filters. The best way to get more out of ITK-SNAP is to get a multi-core CPU, the more cores, the faster most processing algorithms will be. And of course, enough memory for processing large datasets.
However, with all the excitement about deep learning these days, if I were shopping for a machine I would probably get one with a decent GPU, e.g., a mid to high-range NVidia gaming card.
Best,
paul