A good discussion of this problem was presented by Harry Gove in the paper that presented the bioplastic-polymer hypothesis [Gove, Mattingly, David, and Garza-Valdes, Nuc. Inst. and Methods in Physics Res. B, 123 (1997) 504-507].
It would be important to know when the contamination appeared in order to know how much effect it would have on the date. Obviously, if all of the contamination occurred in about AD 33, there would be no change in the apparent age. If all of the contamination appeared at the time of the fire of 1532, 79% of the carbon in the Shroud would have to have been from the contamination and only 21 % from the original cloth in order to give a date of 1357.
This problem applies to all postulated types, amounts, and ages of possible contamination. Contamination had little or no effect on the age reported by Damon et al.