You could create your own custom efx.
Create new efx (or copy and paste existing one and edit it) so it doesn't show any visual effect, leave its play animation and make it loop. Then add sound effect to this "model".
Basically you will have model with no planes that will just loop "stand" animation and you set up that when "stand" animation is played a sound effect is played as well.
Save model, import it. Then attach the model to the unit.
This way you can attach this model to multiple units or all units of some unit type, etc. without having to use periodic loop trigger (which may be ineffective) or editing the model themselves.
You could look at model of some missile to see how it works - these models use one sound effect for when the model plays "stand" animation and other sound when it player "death" animation. For example the Druid of the Talon missile.