If you've got an SSD connected by a power cord, presumably you could insert an electric-current-meter to see how much power it's drawing, then hook up a speaker to make corresponding sounds.
Maybe also put a temperature probe inside of the SSD's box (perhaps directly on a controller-IC?), then another probe just outside of the SSD's box (or inside of it, but away from the controller-IC?), then use that temperature difference too?
A software solution would probably be easier, but then you'd have to trust the system to give correct information, which I guess would defeat the point.
Someone who'd really want to go at this might make their own controller to place between the motherboard and SSD. But unless it's passive/transparent, allowing the normal SSD driver to be used, that'd seem to require writing a driver for the controller too.
I wish that was an option with SSDs. A little speaker included with the package that I could toggle on. All it does it make fake HDD sounds. Bonus if those sounds match the underlying logical distance and “shape” of the read/write activity.