...I understand that this is generally ok and safe
You are misinformed here.
It is never safe for the third prong of a receptacle to be open, never!
The Underwriters Laboratory's safety
rating on equipment with a 3-prong plug is entirely
based on the ground connection not being open.
Everything has worked fine for years.
I don't doubt this. A ground connection is to provide safety in the rare event that a piece of equipment develops a fault. The longer you go without a fault, the more likely that one will occur.
Computers require grounding for electrical noise suppression in addition to user safety.
Would I be able to simply run a ground wire to this pipe and clamp it in place to effectively ground this circuit?
This would have some degree of effectiveness but I do not
recommend this. The ground connection should be sourced by the main service
so that all grounds are at the same potential, and no anomaly in your plumbing system turns a pipe into a live wire via a faulty appliance.