Is it possible to measure ABRs via a bone-anchored hearing aid?

Yes.

Bone-anchored hearing system (BAHS) patients are typically those with a conductive (or mixed) or single-sided sensorineural deafness. Either of these two categories of patient can be tested either with conventional bone-conducted stimuli (e.g. through a Radioear B71 or B81 bone conductor), or their prosthetic device can be stimulated directly, and the evoked potential system merely measures the response (but does not provide the stimulus). This latter approach has some similarities to that of eABR (electrically evoked ABR) associated with cochlear implant patients.