Yes, continuous exposure to white noise affects neural responses in the auditory system. First, it can alter the tonotopic map in the auditory cortex. Second, it can lead to reduced responsiveness of the auditory thalamus.
Note: this answer is based on animal experiments using extreme conditions, namely a continuous noise exposure for at least a month.
The most striking effect of continuous low-level white noise exposure (30 days) is a dramatic reorganization of the tonotopic map in the auditory cortex (Zheng, 2012). Basically, the normally regular distribution of low-to-high frequency representation in auditory cortex was grossly disorganized in noise-treated rats. The noise-treated rats performed better on a pitch-discrimination task in noise than non-treated rats. They performed worse in a quiet environment, though. Hence, their auditory system had adapted to the noise and was optimized for noisy environments.
In another study it was shown that adult rats exposed to noise (50 days) showed increased long-term-depression (LTD) in A1 neurons of the medial-geniculate nucleus (MGN) (Speechley et al., 2007). The MGN is the thalamic processing centre of the auditory pathway (Rees, 2009). Speechley et al. mention the following, and I quote:
The facilitation of depression observed here [..] suggests that in the developed A1 continuous white noise produces general over-excitation of thalamocortical networks,
resulting in greater LTD induced by low-frequency inputs to the network.
LTD can be interpreted as a long-term decrease in responsiveness of the auditory system to stimulation. Basically it reacts to the white noise by decreasing its activity. They explain these effects by the fact that white noise can act as a mild stressor, with accompanying changes in neuroendocrine activation and immune function. Stress and related hormonal changes may increase corticosteroid levels that facilitating LTD.
Interestingly, in newborn rats, the same treatment resulted in enhanced long-term potentiation (LTP) of the MGN. The authors raise the following explanation, and I quote:
White noise reared animals showed greater levels of LTP relative to rats raised in
unaltered auditory environments. Also, stimulation parameters (single 1-Hz pulses) that induced depression in control animals resulted in robust potentiation in white noise-reared rats, indicating that lack of patterned auditory stimulation during early post-natal life results in a preferential readiness of the auditory thalamocortical system for
synaptic potentiation over depression.
Rees, Encyclopedia of Neurocience 2009:2275-9
Speechley et al. Eur J Neurosci 2007;26:2576–84
Zheng, Front Syst Neurosci 2012;6:1-14