I think it should be possible :)

The Audio Library player is driven by Javascript, so can write a script
that prompts which song for it to play. If you want only one random song,
you could "intercept" which tracks get loaded into the player, to load
only the one you want, or if you want shuffle, you could change the
sorting then allow normal behavior, or you could put the sorting in, as
normal, but use a script that starts on a random track