All true; GFCI wont care about the grounding wire, whether its there or not, carrying current or not. However, the bond on the generator provides a path from EGC to neutral. Perhaps I didnt phrase my question the way I intended: with the bonding jumper on the generator, would current on the building's grounds (which are tied to the generator neutral) cause the generator GFCI to trip? The shop vac the OP plugged in is isolated and did not trip the breaker, which is expected. If the same shop vac was plugged into an outlet fed from the subpanel, wouldnt it trip its breaker?
With the bonding jumper on the generator AND no connection between the generator-driven neutrals and the building neutrals AND no other ground/neutral bond downstream of the generator, any current traveling on the generator EGC will not have a parallel path to travel over the generator neutral, so no trip.
If the shop vac is plugged into a generator driven circuit and does not have excessive leakage current it will not cause a trip whether it has an EGC associated with it or not.
If the shop vac has a three wire connection and enough leakage to trip the possibly over sensitive GFCI, then it could trip the generator breaker.
If it has leakage to building ground or directly to earth, it will trip the generator GFCI even without an EGC in its cord.
the building's grounds (which are tied to the generator neutral)
The only tie between the generator neutral and the building neutral will come from the fact that the building neutral is tied to the building ground which is in turn tied to the generator ground and also therefore to generator neutral. But if the only two bonds are at the generator and at the service panel you can try all you want to find a path for building neutral current to travel on the generator neutral or generator neutral current to travel on the building neutral and it is just not there.