What happens if the ANRB customer goes mobile without an internet connection?
I do this regularly Mike. Basically, it just means that you don't get any Network traffic or updates, but everything that has already downloaded/populated onto your PC will still be available.
So, you will get all the existing aircraft details in NavData.db3, all the routes, all the thumbnail pictures, all the outlines. Quite frankly, if you've been running your RB for a while and don't go too far from your home location, you're going to see all your 'normal' traffic and you won't notice too much of a difference.
Why don't you just switch off your modem and see for yourself.