You can’t use EnvVars in Environment directives. The whole Environment= will be ignored. If you use EnvironmentFile=, then the specified file will be loaded without substitution. So PATH=/local/bin:$PATH would be exactly that, and this is probably not what you want.
Under CentOS7 the following works.
# /etc/systemd/system/nagios.service.d/env.conf
[Service]
Environment="PATH=/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin"
> sudo systemctl daemon-reload
> sudo systemctl restart nagios
> sudo cat /proc/28647/environ
...
PATH=/bin:/usr/local/sbin:/usr/local/bin:/usr/sbin:/usr/bin
...