Indeed there is a difference between balanced wiring and ordinary 3 pin wiring.
One reason is you get double the output voltage which could be important when driving high impedance headphones (300 Ohm to 600 Ohm) as you get 6dB more output this way.
For headphones with an impedance below 32 Ohm the extra volume gain could be less (depends on the device and headphone impedance)
When you have headphones with 4 wires inside (can't always tell from the outside of the cable) that are connected in the 3.5mm plug then the only benefit would be the extra gain.
The case described by
@eliash above is valid when for some reason the iem (which is dual entry by definition) could have a cable where the common wire of both earpieces is somehow joined and the joined cable goes to the 3.5mm TRS plug.
This is an unlikely config but when the vendor only has 2 and 3 wire cabling he could opt for that.
In this case the common wire is the culprit and 'changes' the stereo image for certain frequencies.
The IEM wires are usually very thin and could have a substantial resistance compared to the earphone itself
In the example above the 7 Ohm value is very low and depending on how good the 'sleeve' contact and circuit board inside the device used is it is not unlikely that that resistance could produce audible effects.
In this case balanced most certianly is benefical for this aspect but you probably won't enjoy a higher output power (which isn't needed here anyway).
So the answer is .. yes, it could make a difference, but most likely not with the ie 800 as this has a constant impedance of around 12 Ohm.
In case of the example and when using higher impedance headphones it will be beneficial.
I see no reason not to use the balanced out but it may not be very audible in this case.