Yes, every particle crossing the copper can create an anomalous signal that can switch a 0 to 1 or visa versa. If you have enough of those, the program(s) will eventually crash. On the processors themselves the L1/L2 caches are vulnerable, but beyond that, the ROM could also get corrupted making hard resets impossible even after a crash.

Fiber optic cables aren't immune to this either : http://misspiggy.gsfc.nasa.gov/tva/meldoc/cabass/rad.htm