AAaaahhhh... another electronics thread.

In addition to personal electronics there can also be a few other things causing the issue you experienced and it's not accurate for the pilot to place blame on some personal electronics stuff.

For example, heavy rain can result in static buildup on the airframe if they diffusers aren't connected properly. Or the radio might have chosen that particular moment to die. Or another airplane may have taxied too far and was partially intruding into the IFR caution zone. Or the radio was mistuned. Whatever. I would hope that the AE plane has better electronics than the Cessna 172 that I have pleasure of driving, but if I've been flying using the GPS tuned into the VOR display and then try to land using the ILS but forget to push the "NAV/GPS" toggle button, it will appear as if my ILS is broken. It's been known to happen.

As far as going around... that seems like the prudent thing to do. And assuming that your plane was trying to use an ILS approach, assuming they had been using VORs or GPS to navigate to ORD without problems, they could have then (presumptively) initiated one of those approaches without issue albeit with potentially higher minimums.