Seeing the same issue on High Sierra Macs in our office. This is a new problem that has just started as of the last OSX update. No version of the Anyconnect client works on these machines, however, there is no problem with Anyconnect when running in Parallels.
I have not yet done a packet capture, but it does not appear that in OSX that there is any traffic passing out of the machine to establish the VPN connection. Some setting or configuration within OSX appears to be preventing normal operation of Anyconnect.
