Do I have to connect the grounding electrode at a detached garage to the grounding electrode at the main structure?
Yes, they should be connected so that the power has a set path back to the source. Rods in the ground are there for a direct shot of electricity (lightning.) Connecting back to the source is for actual grounding - to tie in with the neutral and cause a short if any sort of ground fault were to occur. Without this, running the ground rods and electrodes would not flip the breaker in most cases.


(source: nachi.org)