Yes, it is necessary to add stop solution in ELISA plate. When stop solution is added,
it causes a drastic shift in the pH and terminates the ongoing reaction. This will stabilize the color change of the medium and allow a period in which the optical density of the assay can be accurately measured.
For instance, when a standard curve is plotted in ELISA using different concentrations of the standard in order to measure the unknown sample, the stop solution will help to stop the ongoing reaction in the middle of the linear phase of the standard curve so that proper OD readings are recorded which in turn will help to calculate the accurate concentration of the unknown sample.
If you do not add the stop solution, the signal will surpass the linear range of the standard curve and the absorbance recorded will not be proper leading to inaccurate results.