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

Viral infection should not affect your surgical results in general.  If you are concerned it is best to contact your doctor.

Assuming that you are otherwise healthy this viral illness should not effect the growth of your grafts.

 After the 4th day your grafts have
settled into their new location and baring an infection to the scalp it is
doubtful that your Norovirus (which usually affects the gastrointestinal system),
will disrupt your hair transplant.

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.