Apple - Is there a remote desktop solution that will transfer sound output to the client?

RogueAmoeba's AirFoil product may be helpful -- it allows you to send sound from any Mac or Windows machine (or any specific application on that machine) to one or more other Apple devices or Windows PCs on the same LAN.

The product has many features, e.g. a custom video player that ensures the sound your receive locally is in sync with any video you are viewing remotely.

Because AirFoil only streams audio, you can use it in conjunction with whatever remote desktop viewing solution works best for you.

I immediately thought of something like soundflower, and their support page points to a project called jackaudio that may be able to send audio over a local network. This is, admittedly, separate intended functionality from VNC or other screensharing utilities. A smart guy I know refers to this as 'a wonderful third-party opportunity'.
iOS/Pad specific stuff would probably only focus on media, like AirView and StreamToMe.