After a night of troubleshooting, I finally got the stretch goal of my project working. Now, when my alarm goes off, my curtain will automatically open!

Check it out in action:

When the alarm goes off, Sleep as Android uses the Maker channel of IFTTT to send a status to an Adafruit IO feed. The ESP8266 checks this feed, and if it sees an alarm status, it will trigger a digital output which is read by an Arduino. This Arduino then begins the process of operating the servo to open the curtain.

Documentation is coming soon!