Yes, but std::atomic doesn't guarantee that it will use actual atomic CPU instructions, it could use a mutex internally if you use it with a large structure.
std::atomic<enum> will compile just fine if you have a standard-compliant compiler.
In practice, on Intel platforms std::atomic<T> will be lock-free (no mutexes will be inserted internally) if T can be represented as a fundamental type not larger than 64 bit.
enum is always represented as a fundamental integer type internally. In practice, on all common platforms this will be an int (unless you specify otherwise using the enum class syntax).
Therefore, std::atomic<enum> is perfectly fine and will behave as a std::atomic<int>.
It really just comes down to the extra code that would be needed to implement more types for juce::Atomic. But in the near future when we finally ditch C++03 support, the juce atomic class will become a tiny wrapper around std::atomic that we keep for compatibility with legacy code.
Certainly in your own codebases, if you're using C++11 then you should choose std::atomic!