Yes, this is indeed what it does - it snaps to Input Snap Stream Grid (see the Snap Pour tool for more details).
If snapping is requested, all the points located within 6 cells (default) of a Snap Stream Grid cell (or Stream grid cell if Snap Stream Grid is left null) will be snapped onto the closest cell on the stream. If the snapped point is not located in the same catchment as the original point, the tool populates the field BatchDone with the value 2 to flag the input point.
Note
The default snapping tolerance is read from the configuration XML and is set to 6 cells. This value can be modified by editing the parameter HydroConfig/ProgParams/ApFunctions/ApFunction(BatchWatershedDelineation/SnapToleranceNumCells
For some work I'm currently doing, I'm running a select by location on seed points to find all that not within 150m of a synthetic flow line feature - I then visit them one by one and edit them by hand on to the cell I want - and set SnapOn to zero. These points are the ones whose drainage area is too small to land on a synthetic flow line - so I am moving them to a high-fac cell to delineate from.