Yes it does, what does the sun do, it emits light, and it emits charged particles, these plumes of gas are many times larger than our planet. If you think the sun has nothing to do with the weather you are literally an ignoramus. Weather is driven by energy, the atmosphere absorbs energy, the ground absorbs it, radiates it, the energy isn't distributed evenly which creates differences in pressure which drives trade winds, etc. Hurricanes and solar flares are strongly correlated. The sun doesn't drive weather...absolute retardation.