No. Norton Security is available as a 32-bit application only. It does have both 32-bit and 64-bit drivers though, depending on the operating system platform it is installed on. As it stands now, Symantec’s developers only create x64 binaries where required, for the remainder they use x86 binaries. The reason for this is that (as per Symantec’s developers) there is no benefit to using x64 binaries when x86 binaries work equally well. The only applications that benefit from x64 are applications with more than 3GB memory utilization requirements, and these apps (Norton Security and Norton Security with Backup) do not fall in that category.
So, in order to be able to support both 32-bit and 64-bit environments, Norton Security has to carry both versions of required DLLs. For the rest of its files, unless required, they’re 32-bit, and the application itself is marked as 32-bit as well.
In short, Norton Security as a 32-bit application is sufficient in both 32- and 64-bit environments.