2003 Volkswagen Passat turbo charger

How fast does a turbo charger reheat? Can you drive 400-500 miles with the engine light on and possible turbo issues?

Question 1, I don’t know.
Question 2. Have the codes read and find out what the problem is, then your question might be answerable. You might have a serious problem that needs to be addressed immediately or risk severe damage to your engine.