Would there really be all that much evacuation? Pretty sure the saucer section contains all the living and civilian areas, the laboratories, main sickbay etc.
The Stardrive section seems to consist mostly of engineering and engineering-related parts, the battle bridge, and probably a secondary sickbay and other redundancies (like emergency quarters) that would be used in case of a longer separation from the saucer (or a destruction thereof)
So to me it seems evacuating the Stardrive Section would mostly involve just getting the engineering teams to the saucer section, and whoever performed other tasks in the stardrive section during that time.