If your HDDs (or any other equipment) are inside a metal enclosure (like a standard PC case) and you unplug all external cables from it, it will be just fine. Any kind of metal enclosure with holes smaller than the wavelength of the radiation acts like a Faraday's cage, external EM field will not be able penetrate it. Solar storm generates a low frequency (very long wavelength) electromagnetic waves, so even a steel reinforced concrete construction (or any other metal net) with a good grounding would completely stop it.