CMGs don't need go back to medical school for MD but have to pass board examinations in order to be qualified for applying residency programs in USA.
In general, residency programs don't accept CMG without GC (they want to see you are good enough to be a US physicians .......all depends)
You take step 1 and step 2 and clinical assessment test before applying for residency, step 3 board exam before or after residency. There is 7 years limitation from the time you taking step 1 exam to step 3.
Therefore, people take board exams after they get GC.
Hope that I answer you questions.