Does a geomagnetic storm visibly deflect a compass?
You can definitely see a large geomagnetic storm with a compass, if you have the timing to catch one and the patience to sit and stare for a few minutes.

If you look at these minutely measurements from Lerwick observatory for one of the more recent large storms (the 2003 Halloween storm), you can see a roughly 4.5 degree swing in declination (labelled "D", the horizontal magnetic field angle to geographic North) over about 15 minutes at about 07:00. "I" is inclination, vertical field angle to the horizontal plane, "F" is total intensity of the field.




  Lerwick (LER) based on 1-minute definitive data 2003-10-29 shows plots for D and I in degrees and F in nT. D shows a dip to -2 degrees in the hour before 07:00 UT and then a sudden rise to about +1.5  degrees at about 07:00 with spikes to +2 degrees.


It will depend on where you are as to how big this change in the magnetic field is, and how big the storm is. For this storm, the UK geomagnetic observatory network gives a good idea of how the effect seen depends on where you are.




  Compass angles (positive West, negative East) measured at BGS Lerwick, Eskdalemuir and Hartland observatories during 2003-10-29 and 2003-10-30. The the biggest change is seen at Lerwick, a smaller change is seen at Eskdalemuir further to the south (further away from the auroral zone where the field changes are occurring), and a smaller change still at Hartland.