That will probably not work, because the ESSM uses radar semi-active illumination, while the Seahawk is only able to provide laser illumination (the Seahawk’s search radar does not support SARH illumination).
Don’t forget to check the new submarine tutorials; 1.1-1.4 are already bundled with the current version and another four are available here: http://www.matrixgames.com/forums/tm.asp?m=4459109 …and will be included on the next public update.