From the datasheet the atmega328 will only reliably register a low on the a digital pin when the voltage is below 0.3v in a 5v system. It has to be above 0.6V to register as high.
If your signal is reliably staying above 0.6V while fed from the MP3 player and is reliably dropping below 0.3v when the signal ends then you could convert to digital input.
Unfortunately a multi meter with a slow update rate may not be able to detect if those voltages are stable or not. If they're not stable then you could get excessive triggering on a digital pin. You would need some kind of latching circuit to workaround a unstable signal and seeing that your project is already installed that is probably out of the question.
You're probably better off staying with the Analog and using a software latch.
Because you're being proactive in trying to set up something prior to your site visit you really should set up something that logs the analog values to serial so you can get an understanding of what the signal looks like. If it's clean high/low then you can use pin interrupts to trigger your arduino to fire the relays. If the signal is messy then you can analyse the serial data to select an analog threshold value that you can include in your sketch.