Not all the time... It's a little more complex than straight forward cause and effect. I think maybe it has to do with the global energy budget of the Earth and the amount of energy the atmosphere and the planet is able to "absorb" at the magnetic poles. Sometimes intense storms are associated with major Earth activity and sometimes they're not. All I know is I tend to dream a lot more during periods of intense geomagnetic activity.

And there is actually evidence for such a phenomena of the magnetic field affecting dreams.

[link to www.newscientist.com]

Looking for an explanation for recurring nightmares of leaving the house without your trousers on or losing your teeth? New research suggests you can blame the Earth's magnetic field, rather than a repressed childhood.

Darren Lipnicki, a psychologist formerly at the Center for Space Medicine in Berlin, Germany, found a correlation between the bizarreness of his dreams, recorded over eight years, and extremes in local geomagnetic activity.

Other studies have tied low geomagnetic activity to increases in the production of the melatonin, a potent hormone that helps set the body's circadian clock. So, based on anecdotal evidence that melatonin supplements used as a sleeping aid can cause off-kilter dreams, Lipnicki wondered whether local magnetic fields could induce the same effects.

*snip*
Lipnicki looked up daily geomagnetic activity in Perth, Australia – his home at the time. A scale called the k-index quantifies local geomagnetic activity, and he included only days that scored on the extremes of this index. This whittled his dream log down to 66 days of low geomagnetic activity and 70 days of high activity.

Using these figures, Lipnicki uncovered a statistical correlation between dream bizarreness and geomagnetic activity, with freakier dreams occurring on days with the least geomagnetic activity.