Perhaps, but I'm not sure how you fix the problem of the deposits you already made and perhaps correct the plan agreement to show the plan as established under the S corp. If the plan was properly established under the S corp, you might only have an accounting problem within the S corp to sort out so that the W-2 reports the proper amounts in boxes 1 and with code D in box 12.
A W-4 has nothing to do with establishing payroll deductions for the purpose of elective deferrals to a 401(k). You must make a written request to your S corp to make any elective deferrals to a 401(k), either as a lump sum or as periodic deferrals, and no elective deferrals are permitted until you make the election. The S corp will need to retain a copy of that election dated prior to any deposits of elective deferrals.
