Even without inter-carrier HD voice support, simply running HD codecs on both air links will produce a noticeable increase in call quality. Traditional cellular codecs transcode your calls to a bitrate and quality that is lower than that of a regular landline, and this happens on both sides of the call separately since it has to traverse the PSTN. But with HD voice codecs, the cellular codecs are actually higher quality than landlines, so the PSTN is the quality bottleneck.
In other words, today, a call between two HD voice capable handsets across cellular carriers should be of comparable quality to a call between an HD voice handset and a landline.