I don't think so. Other dogs in the house would likely get it directly from the puppy so washing objects probably wouldn't help. People do not get this strain of the organism so that's not a worry. The puppy itself will not get reinfected immediately and the organism will die out on surfaces. At least that's my best guess from a human medical perspective.
When my Doodles had kennel cough the Vet did not indicate that we had to do this. When they had giardia, she did tell me that everything had to be washed in hot water, but not with the kennel cough.