Sure, but you are limited by the age of the child. There are limitations in the ABR system in terms of how low responses can actually be visualized in the waveform, and consider also how they would have masked appropriately since they are already at the limits of the system in the other ear.
Even after ABR, up until 3-5 years (depends on the child), you aren’t getting true thresholds with children you are only getting minimum response levels. So, for example, a 2 year old with perfect hearing may not respond in the booth well behaviourally to anything under 20 dB HL even though they can hear down to -10 dB HL, so once you get that through air there’s no point in doing bone. The auditory attentional system is still developing at that stage. Also, their overall ability to stay still and pay attention still sucks, so you don’t want to test down to soft levels if you are already within the realm of normal because you risk losing their attention and only getting results that day for one frequency in one ear. Bilateral masked bone at four frequencies in a 4 year old is a banner day.
An interesting note on the developing auditory system: I’m sure you’ve noticed that in adults if you are at threshold with one frequency and then suddenly jump to another frequency (or to the other ear) at that same level the adult will often miss it until you prime them to pay attention to that frequency (or ear) with a louder presentation. The adult auditory system attends to a particular tone and makes the ear (mechanically causes the ear to be) more sensitive at that frequency and less sensitive at others. This system isn’t in place in young children yet, so around 5-6 years of age you can often get them down to threshold and then just skip right across frequencies and from ear to ear at that level and they will respond the whole way along. It’s neither here nor there, just a nice demonstration of development in action.