It will make make a huge difference, just like a super or turbo conversion would. Coupled with the fact that you are carrying some highly flammable gas and the fact that it gives a huge boost of power in one go usually.
A lot of insurers would even touch you once you mention NOS fitted, for road use or not.
If you have undisclosed NOS on the car and claim, yes it is very unlikely that the claim would not go through and you would probably be refused cover, which is about as bad as it gets.
Always good to get some information from the people who know
Like i said i can see why Nitrous on the road would make a difference but if its not installed for use then it shouldnt matter IMO. The gas isnt highly flammable, and the cylinder wouldnt be installed anyway.
Ah well, whats this under body kit?