I think that you are looking for a larger waveform due to binaural interaction that perceptually would be considered as binaural summation. If you were to look at the P300 wave, you should see the effect. Binaural summation is a higher function than he brainstem. See Neurosci Lett. 1997 Jan 24;222(1):37-40.
Binaural interaction in the human brain can be non-invasively accessed with long-latency event-related potentials.
Lavikainen J1, Tiitinen H, May P, Näätänen R. for a start.
What do you mean by "reliable"? If by reliable you mean present and easily detectable in all normal listeners, a main issue with the ABR BIC is that it is small in amplitude and sometimes hard to see in background noise (especially since the subtraction procedure results in the waveform noise increasing 1.4X noise). One must ensure sufficient trials are recorded to ensure waveform noise is 1/3rd to max 1/2 the amplitude of the BIC.
As already noted, BICs for MLRs and especially N1-P2 are much larger in amplitude. Numerous pubs have shown this, for example:
Picton, T. W., Rodriguez, R. T., Linden, R. D., & Maiste, A. C. (1985). The neurophysiology of human hearing. Human Communication Canada, 9, 127-136
McPherson, D. L., & Starr, A. (1993). Binaural interaction in auditory evoked potentials: brainstem, middle- and long-latency components. Hearing Research, 66, 91-98.
Fowler, C. G., & Mikami, C. M. (1996). Phase effects on the middle and late auditory evoked potentials. Journal of the American Academy of Audiology, 7, 23-30.
If by "reliable", however, you refer to how well it determines normal vs impaired binaural processing. Well, there are few data concerning this and certainly far too few data for it to be used clinically. See for example:
Levine, R. A., Gardner, J. C., Fullerton, B. C., et al. (1993). Effects of mulitple sclerosis brainstem lesions on sound lateralization and brainstem auditory evoked potentials. Hearing Research, 68, 73-88.
Pratt, H., Polyakov, A., Ahronson, V., et al. (1998). Effects of localized pontine lesions on auditory brain-stem evoked potential and binaural processing in humans. Electroencephalography and clinical neurophysiology, 108, 511-520.
Delb, W., Strauss, D. J., Hohenberg, G., & Plinkert, P. K. (2003). The binaural interaction component (BIC) in children with central auditory processing disorders (CAPD). [Comparative Study]. Int J Audiol, 42(7), 401-412.
He, S., Brown, C. J., & Abbas, P. J. (2012). Preliminary results of the relationship between the binaural interaction component of the electrically evoked auditory brainstem response and interaural pitch comparisons in bilateral cochlear implant recipients. Ear Hear, 33(1), 57-68. doi: 10.1097/AUD.0b013e31822519ef
Wave III is from cochlear nucleus. In this nucleus we do not have much binaural processing. Actually first stage of binaural processing is SOC (superior olivary complex). Before SOC we don't have binaural interaction.