Excellent question, Atkinson.
I understand that the normal depth is calculated considering the cross section covered by the boundary condition line.
Therefore, I understand that for this boundary condition the magnitude of the line has an impact on the local water depth results (at least local, since far enough upstream this may have little or no impact). Also note that the size of the cells embedded in the boundary condition line impacts the accuracy of the calculation.
On the other hand, if you had a discharge curve instead of the normal depth as a boundary condition, the local levels should not be impacted, but the flow approach conditions should be, since not incorporating the flood area can cause unrealistic contractions in flow, although water levels may be adequate.
It is also important to keep in mind the distance between the downstream boundary condition and the areas under study. If this distance is quite large, the boundary conditions may not significantly impact your analysis.
Finally, I would say that the downstream boundary condition can impact your study area more or less depending on the simulated hydrograph, the bottom slope etc., since all this impact in the general flow conditions. Abrupt hydrographs may suffer greater distortion than gradual hydrographs, e.g.
After all this, one might ask: why not make the boundary condition line a little larger than is really necessary? Assuming that there are no local obstructions near the flow exit, this may be an aspect to be considered.
Hope this helps.