Hi Robert.
Fusion Sim will use multiple cores for meshing and solving when these operations are run locally, but it doesn't use multiple cores all the time. Meshing can use more cores if you have lots of parts, but it will only use one core if you have a single part. The solves you are able to run locally will only use up to 8 cores, but only at certain points during the calculation. You can also only do one local solve at a time.
Nonlinear Static, Event Simulation, and Shape Generation are cloud only, so your machine specs won't come into play when you use those study types.
Generally you are better off getting CPU with a higher clock speed for Fusion, as there are many operations which do not benefit from multiple cores. For example, you might be better off with an 8 core, 3.4+ Ghz system, than with a 16 core, 2.2 Ghz system.
Hope this helps.
Rob McMillan
Software Architect, Fusion Simulation
Autodesk