Hello Chris,
The main potential benefit of AVX-512 to Hauptwerk would be that it allows more CPU registers, thus potentially reducing stress on the CPU cache and RAM, especially benefiting polyphony. It may also allow more efficient convolution reverb, since more data can be processed in a single instruction.
However, Hauptwerk doesn't currently (v5 or v6.0.1) have a dedicated AVX-512-optimised executable included in its installer, due to a possible problem that was found with it on one one particular AVX-512 CPU model. Hence for Hauptwerk v5/v6.0.1 currently the AVX-2-optimised executable will be installed instead (which is definitely safe with on all AVX-512 CPU models). In the longer-term, we do hope to include a dedicated AVX-512-optimised executable, which would gain the full benefit from an AVX-512-capable CPU.
I hope that helps.