There are two different phrases that you are mixing up. Additive White Gaussian noise is something that is present in mathematical models of communication systems, even those classified as communication systems operating over acoustic channels or fading channels etc because this noise is not actually something that the channel adds, but rather something that models the thermal noise in the receiver, that is, the electronic components that actually do the stuff that dsp.SE folks write equations about. The phrase Additive White Gaussian noise channel describes a channel in which the only impairment is that the received signal gets white Gaussian noise added to it: what is transmitted is exactly what is received with the exception that white Gaussian noise has been added to the transmitted signal; no filtering of any kind, no multipath, no fading, no reverberation, no psychoacoustic addition of harmonic overtones where none existed before, no intersymbol interference, no jamming signals, no adjacent-channel interference, no multiple-access interference, nothing. All mathematical models of channels should include Gaussian noise as a stand-in for thermal noise, though in several instances, the thermal noise has little effect on the performance because it is so weak compared to the other channel impairments that it can be ignored for simplicity of analysis and exposition.
Turning to the questions asked, Yes, it is possible to design matched filters for channels that are not described as AWGN channels but the criteria used can be different and the analyses can be different too. As described in this answer a matched filter can be viewed as an LTI system designed to maximize the output signal value at a specific time instant but that might not the optimum thing to do for other noise models or other channel impairments. For such channels, a nonlinear filter which produces a smaller output but provides better noise suppression or better removal of channel impairments might be preferable to the canonical matched filter that works perfectly with AWGN but is suspect in other cases.