There is no problem running 32-bit applications under Mountain Lion. They will work just as well as they did in Leopard, Snow Leopard, and Lion. The issue with 32/64 bit code is that any >kernel extensions< (primarily utilities, and programs that interact with specific hardware) that run on OS X must run in the same mode as the kernel, i.e. a 32-bit extension won't run on Mountain Lion because it has only a 64-bit kernel.
Family Tree Maker does not install any kernel extensions so this is not an issue.