Even though I'm old and have some hearing-loss from the military and outdoor activities, I am able to tell the difference between sound files encodings on familiar music. Also, I can hear on my Macbook Pro when the amplifier circuits get power - there's an audible hiss.
If I can hear it, someone younger can almost certainly hear it, if they've trained themselves in how to listen and don't try and multitask.
One thing that hasn't been discussed is that of power. Does the Lightning connector have the ability to pass enough current to the external DAC to drive large over-the-ear headphones and generate respectable bass without distortion? Or will the headphones require it's own battery (AAA or rechargeable)?