The shape of the model does not change when doing the manual realignment. If you care about the accuracy of your elevations you need to use lots of overlap and use Map Pilot's Active Connect mode to get the best model possible. You want your entire overlap report to be blue. Also when a large section of the survey area is water you will want to include a larger area around the top to provide more context.
From there, the GCPs will apply a linear offset based on the differences between the generated DEM and the surveyed points.
You can check your GCPs vs the model in the DEM file using GIS software such as QGIS.