You would uninstall a lot of other stuff that depends on it of which cairo-dock is the most prominent on Elive.
In that sense, it might be an idea to look for another dock to have available for E16.
"nmtui" is just a terminal ncurses interface to NM as the name shows, so: No nmtui will not be usable as that will be removed too.
Since "network-manager" is a daemon .... you could see if stopping/de-activating network-manager makes any difference in your case. On my machine it only seems to work if network-manager hasn't already kicked in somewhere.
You can do that with:
"sudo /etc/init.d/network-manager stop"
"sudo service network-manager stop"
Obviously you can
start or see the
status of the service in a similar fashion