The autothrottle should be completely switched off for a SE approach and SE go-around (says so in the Boeing FTM) - so the question of it being available for a SE go-around never arises.
Which raises a similar question. Why is it that the autothrottle is switched off as part of the recall actions associated with an engine fire drill at 400 feet after lift off - yet not switched off until the item is read as part of an engine failure (flame-out at V1)and shut-down drill which Boeing say should not be actioned until the aircraft has been cleaned up and max continuous set?
Seems to me that when an engine fails the auto-throttle should be disconnected immediately?