Sickness one week after hair transplantation, will this impact my final result?

If it's been a week you should be fine. At this point it would take significant physical stress to harm your grafts, so illnesses in general are not a risk to your transplant, except a scalp infection or something in that vein. 

Having the norovirus should not impact the results of the hair transplant. Keep well hydrated and hope you feel better soon.