Answering the question directly, your intuition is right that you'll want to limit the ways that your machine can be exploited. Since this is a Dell machine, I would think iDRAC is well suited to be the control mechanism here. iDRAC can accept SNMP commands and some newer versions can receive REST API calls.
But stepping back for a moment, is there any reason why you cannot configure the "AC Power Recovery" option in the system setup to boot the machine when power is restored? The default behavior is to remain as it was but you can configure it to always boot up.
From your description, it sounds like your APC unit notifies the server that the grid is down, which results in the OS shutting down. Ostensibly, the APC unit will soon diminish its battery supply and then the r320 will be without AC power. When the grid comes back up, the r320 will receive AC power and can then react by booting up, if so configured. Is this not feasible?