Had a platysmaplasty and mini face lift. Have had a cough. Will this undo the good work the surgeon did and spoil my neck lift?

Coughing involves more the diaphragm and abdominal muscles and does not typically include the platysma contractions unless it is associated with a lot of  straining.  It is not likely to affect the outcome of your surgery.
If the  platysma muscle bands are still noticeable following your surgery it  generally means that platysmaplasty was not sufficient to control the neck contour. There are additional options to control the  bands, and a formal assessment would be necessary. The best first step would be to discuss this matter with your surgeon. If you feel this is not likely to solve your problem, a second opinion would valuable. 
By and large, the platysma bands can be controlled even when the muscles are used very actively.

Cough does not usually alter the results of a surgical procedure. Neck lift is a procedure where the skin is tightened and lifted up to decrease the skin folds. Perhaps cough may affect the scars but it doesn't seem to have any significant effect. The best resource of information would be your board certified plastic surgeon as he/she knows your condition best.