I did some tests, and can confirm that with n-m 1.2.6-0ubuntu0.16.04.1 my local DNS (sent via dhcp to the machine) is also added to the DNS server list when the VPN is established:
Aug 31 20:36:32 31-64 dnsmasq[1118]: setting upstream servers from DBus
Aug 31 20:36:32 31-64 dnsmasq[1118]: using nameserver 10.0.5.5#53(via ens3)
Aug 31 20:36:32 31-64 dnsmasq[1118]: using nameserver 10.172.64.1#53 for domain private
Aug 31 20:36:32 31-64 dnsmasq[1118]: using nameserver 10.172.64.1#53 for domain internal
(...)
The line about using the 10.0.5.5 nameserver does not appear the logs when using n-m 1.2.2.
As far as I can see, there are two other bugs filed about this: bug #1671606 DNS server from vpn connection is not being used after network-manager upgrade to 1.2.6-0ubuntu0.16.04.1 bug #1688018 DNS server from vpn connection is not being used after network-manager upgrade to 1.2.6
I did some tests, and can confirm that with n-m 1.2.6-0ubuntu0. 16.04.1 my local DNS (sent via dhcp to the machine) is also added to the DNS server list when the VPN is established:
Aug 31 20:36:32 31-64 dnsmasq[1118]: setting upstream servers from DBus
Aug 31 20:36:32 31-64 dnsmasq[1118]: using nameserver 10.0.5.5#53(via ens3)
Aug 31 20:36:32 31-64 dnsmasq[1118]: using nameserver 10.172.64.1#53 for domain private
Aug 31 20:36:32 31-64 dnsmasq[1118]: using nameserver 10.172.64.1#53 for domain internal
(...)
The line about using the 10.0.5.5 nameserver does not appear the logs when using n-m 1.2.2.
As far as I can see, there are two other bugs filed about this: 16.04.1
bug #1671606 DNS server from vpn connection is not being used after network-manager upgrade to 1.2.6-0ubuntu0.
bug #1688018 DNS server from vpn connection is not being used after network-manager upgrade to 1.2.6