If ViM can be run with NOPASSWD via sudo, then commands can be executed as admin using the ! prefix.
However, if a non-standard shell is set in /etc/passwd, Vi and ViM may not be able to shell out with :shell or execute shell commands with !. This is because these apps are attempting to execute $SHELL (in the case of :shell) or $SHELL -c $COMMAND (in the case of !).
Fortunately, Vi and ViM can be set to override the default $SHELL using :set shell=/bin/bash.
(Exotic shells in /etc/passwd can also cause commands executed via ssh to fail for the same reason.)