By default, the NAB adapter simply works for me, without Cisco AnyConnect running.
But DNS lookup failed when Cisco AnyConnect is running, this is due to a critical bug in Ubuntu 12.10+, "bug 1048783: network name lookups broken in NAT network adaptors". See more details at, https://bugs.launchpad.net/ubuntu/+source/virtualbox/+bug/1048783
To workaround this, you would need to run the following cmd to use the host DNS lookup,
From an window command prompt (with VMNAME replaced with your VB name, e.g. "Ubuntu"),
cd "c:\Program Files\Oracle\VirtualBox"
VBoxManage modifyvm VMNAME --natdnshostresolver1 on
BTW, I have "NAT" by default for the 1st adapter, and a "Host-Only" for the 2nd adapter to get around the limitations with NAB only adapter. This setting works perfectly for me.
Make sure you reboot the virtualbox and save the state to preserve the previous settings, not only a power off.