So, yes and no.
WebAudioPlayback is private so you can't override it, and the access modifier is only for properties so you can't access the class through WebAudioSound. So I copied the code from WebAudioPlayback and made a new class with a position property in the constructor. Then in the constructor change the call to WebAudioSound.start to:
if (_sourceNode.start != null) {
_sourceNode.start(WebAudioSound.ctx.currentTime, position);
} else {
_sourceNode.noteOn(WebAudioSound.ctx.currentTime, position);
}
So to start the sound:
new MyWebAudioPlayback(webSound, volume, loop, positionInSecondsFromStartOfFileToStart);
Haven't done a custom version for HTMLSound/HtmlPlayback yet, but assume it will be similar.