From the answer you linked to:
For SHA-1 or SHA-256, computation entirely consists in 32-bit operations on a handful of registers, so a password cracker will run without doing any memory access at all, and full parallelism is easily achieved (I did it on my GeForce 9800 GTX+, and I got about 98% of the theoretical maximum speed with a straightforward unrolled SHA-1 implementation).
What that tells us is that it is fairly easy to get big performance gains on SHA-256 (which also implicates SHA-512) using a GPU. The question then is, does ShaCrypt do anything special to slow GPU's down?
Looking through the example source code you liked to, it doesn't look like it. What I was looking for was a large (a few kilobytes) data structure that would be constantly accessed and modified. That doesn't exist from what I could see. Sure, there are data dependencies, which would slow down a single password calculation, but nothing to prevent parallelization of multiple passwords.
On an interesting note, there are JtR patches which would give you ShaCrypt GPU capabilties in John the Ripper. I was unable to find performance numbers, however.