Yes, if the sheet is finite, the charges on the edge wud play a role in calculating the electric field. And the calculation of electric field by a finite sheet wud get more difficult/complicated due to irregular/random direction of field by the charges on the edges.

See the figure. U will easily get it.

The first sheet is infinite so the field by it is uniform everywhere whereas the second sheet which is finite, the direction of field by it is NOT uniform everywhere due to the charges on the edges.