You'll get an Error: Windows 7 64 bit driver not signed.
This says already what the problem is.
All 64 bit versions of Windows from Vista through Windows 7 must use signed drivers. There is a workaround. You'll have to hold the F8 key while booting. You'll see a menu which provides you a choice to run without driver checking. One of the options of this Safe Mode boot menu is to permit unsigned drivers. This will allow those drivers to be used. Every time you want to use a program that requires an unsigned driver you have to have to use the F8 key on boot up, no way to switch to a permanent version. And while doing that say a big thank you to Microsoft.
Your information is generally outdated. That is only true for some of the (very few) drivers that have not been updated yet. Most SDRs, including Flex Radio SDRs, now have signed drivers so there is no need to use the F8 key bypass. There is absolutely no reason not to use the 64 bit version of Windows 7 now, especially when it allows you to make use of > 3 GBytes RAM where Windows 7 32 bit does not.