You can install SIM 7.1.x on an x86 or x64 platform, however the products list will be filtered based on the platform on which you've installed the SIM. When we installed the SIM on a x86 machine, only the < 7.0 products were available for selection. After installing the SIM on a x64 machine we could then see the 7.1 products.
This did present some challenges in our environment, as we typically created an installation package from the SIM on a "hot" (internet-connected) workstation and then transferred the package to our server. These hot boxes are currently XP 32-bit, so when we installed SIM 7.1 we could not select the 7.1 products in order to create an installation package.
It would be good if you could at least create an installation package for any SIM-installable product on any platform (unless you can and I've missed something!). The installation process for each product should be able to handle its own system requirements check.