If you can clarify who they need to register it with, that would help.
Presumably they have already registered their domain name or they couldn't be using it. If they aren't receiving any money then the tax office doesn't need to know (although if you're making a loss it is useful to tell them for the offset, and if you're making a profit you'd better tell them!). Equally, they'd better have registered the store software if it is commercial, or they might not find themselves making a lot.
If you are talking about registering a business, like a limited company, it depends on whether the site is likely to take off. There are a lot of extra costs involved with being a limited, although it gives legal protection and shelters the owner's assets in case someone sues them or the business goes bankrupt. Personally I am a great believer in limited, but it is a matter of scale. If the site is simply selling granny's knitting patterns, she might do better to sell through Etsy. If its going to be the next Amazon, registering a business early would be a good idea.
How much effort and time do they want to put into it, and how long is the site likely to run?
