Ubuntu >= 15
nmcli device show <interfacename> | grep IP4.DNS
Ubuntu <= 14
nmcli dev list iface <interfacename> | grep IP4
In my case, <interfacename> is eth0, which is common, but not always the case.
See if this is what you want.
I think resolv.conf is actually used indirectly, because the network manager creates the server that listens on 127.0.0.1, but I was told that this is an implementation detail that should not be counted on. I think that if you enter DNS addresses before this entry, they might get used, but I’m not sure exactly how this works. I think it’s best to use the network manager in most cases, when possible.