No, you are incorrect, you aren't supposed to be facing any downtime with the procedure you describe. (Nginx can do not only configuration reload on the fly without any downtime, but even the upgrade of the executable on the fly, still without any downtime.)
As per http://nginx.org/docs/control.html#reconfiguration, sending the
HUP signal to nginx makes sure that it performs a graceful restart, and, if the configuration files are incorrect, the whole procedure is abandoned, and you're left with the nginx as before sending the
HUP signal. At no point should any downtime be possible.
In order for nginx to re-read the configuration file, a HUP signal should be sent to the master process. The master process first checks the syntax validity, then tries to apply new configuration, that is, to open log files and new listen sockets. If this fails, it rolls back changes and continues to work with old configuration.
service nginx reload or
It will do a hot reload of the configuration without downtime. If you have pending requests, then there will be lingering nginx processes that will handle those connections before it dies, so it's an extremely graceful way to reload configs.
Sometimes you may want to prepend with