My understanding is that GECs are not _intended_ to carry current. This is the reason for all of the requirements about a _single_ bond between the _intentional current carrying conductors_ and the GEC.
However the _reality_ is that there are multiple bonds all the time. The common example is in residential service, where multiple residences will all share a single transformer, and _each_ residence will have its own grounding electrode, its own GEC, and its own ground to neutral bond at its own main disconnect. In these circumstances, you can expect to have at least some, and perhaps considerable, current on the GEC. Especially when the grounding electrode is the water service pipe, and the common underground piping system is itself metal. My 'hear-say' understanding is that smart plumbers place a jumper cable across water pipes prior to cutting them.
Also, even in a 'perfect' system where the SDS has a single ground bond with no galvanic parallel path, you will have some slight current on the GEC because of capacitive coupling between the system (and loads) and earth. The capacitive coupling of the various phases will tend to balance out, but any asymmetry in the system leads to just a bit of capacitive coupled current on the GEC.
-Jon
