Of course she has ear. The real question is, why she is wearing the equipment?
So far there's been no speculation I've seen, but Millennium does tend to have a soft mecha musume theme going to many of its characters. Yuuka has the belt and those triangle hair ornaments of hers. She, Noa, and Rio all have mechanical-looking halos. Utaha has floating "rabbit ears" (similar to KanColle's Murakumo) as part of her halo. Aris gets a railgun (and later a powered exoskeleton similar to Toki's, if the PV for Vol. EX is any indicator). The color palate of many of them loosely evokes the image of a Gundam or any other mech from the franchise.
My personal spculation is that they're just an augmented reality eyepiece, something she can lower in front of her to more closely analyze samples, and I wouldn't be surprised if there were wireless communications devices in there. This in turn makes me surprised that nobody's drawn Noa crushing her headpiece like Vegeta (in)famously did as far as I'm aware, even though the joke is right there. Maybe people are above it.
