Yes, they can. This last eruption was EXTREME, the highest rating on the solar "richter" scale.
Check out this site:
http://www.sel.noaa.gov/SWN/
There are explainations of what each level of rating means, and the possible effects. Keep in mind that much depends on how direct the blast is when it hits the Earth's atmosphere.
This one has Auroras as far South as Texas!
FWIW
Scott