Yes the light will go out eventually if the repair fixes the problems. Properly done the adaptations should be cleared. Untill the adaptations readapt I would avoid any energetic driving. It is possible to set other fault codes till it does readapt. It will readapt in probably ten miles enough for driving purposes. What will happen is that because of the old AMM the car will run too rich (they all fail lean on the late style AMM) as it will have the correct sensor reading plus the correction used to run with the old unit.

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Steve Brotherton
Continental Imports
Gainesville FL
Bosch Master, ASE Master, L1
33 years MB technician