That is not a stupid question, it is actually quite difficult to answer.
Short answer, such a faraday enclosure won't do as much against this type of radiation, but your hardrrives should be fine either way.
A microwave oven is optimally shielded for around 2.4 GHz. That is a very very high frequency compared to the solar flare. At lower frequencies, the shielding isn't as optimal and will only yield a minor reduction.
The solar flare puts some dents into the earth magnetic field, that swing back and forth at a much much lower frequency. This causes currents in the mesh of wires we put on top of the earth to power everything.
This current then overloads most systems and destroys electronics on the substations level. Transformers blow out, everything with long wires stretched over a few hundred Kilometers can accumulate a ridiculous unwanted current. Protecting against this is difficult and expensive, so a lot of stuff goes byebye.
Your hard drive lying unconnected in the sun, will feel like it's raining lots of very tiny magnets. It will respond with a tiny surface current, but that would be it.
This should not erase the data.