NAT doesn't need an adapter. What you see, is a GUI bug. If you would switch to a different attached mode, and then switch back to NAT, you will only see the option to generate a MAC address and if the cable is attached or not. VB will use the default gateway and the primary DNS server of your Host for Guest internet. If the primary DNS isn't working, the Guest won't have a working DNS. See the
Forum Posting Guide for some help on that.