No. Natural disasters are inanimate events. Evil needs animation, or life within which to carry out whatever it is that evils "purpose" is.
To you, what distinguishes evil events from bad events? We agree that natural disasters can be bad, correct?
The Holy Spirit, IMO and Belief, is everywhere...without limitation...
while evil disembodied spirits need bodies in which to animate their purpose.
So, if the Holy Spirit is living inside of every virus, harmful bacteria, volcano, lightning bolt, asteroid, tidal wave, etc, is it animating them with its own purposes?
Also, can humans be evil on their own accord, or only via demons?