As in most things, it all depends...

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If you have conventional, internal regulated, alternator it would probably need an initiate signal from the key on or PCM and then it would run on it's own.
If it is a modern, PCM, controlled one, the field current is supplied or controlled by the PCM so it would need that full time. The current is also based on controlling output for accessories turn on, recover energy on coast, etc based on model.
On a Chevy it appears the change came in the 2007/2008 model change. Our 2007 can with an internal regulated alternator, but it appears the 2008s came with a PCM controlled alternator.