Can a computer transmit packets via high-frequency sounds broadcast over speakers ?
Sure. If a mic can pick up the sound and a speaker transmit the sound, it's possible. There's many, many methods of transmitting data via sound. Fast methods are complicated and require optimum conditions, but very slow methods such as PSK used in 300 baud modems are more robust.
Most PC's can create sounds 20-20KHz and beyond. I don't know the maximum frequency of the standard PC speaker but it can go pretty high. Most people can't hear very well above 15KHz ... but I'd be surprised if your average PC mic picks up frequencies outside the normal vocal range (4KHz) very well.
Of course, no OS has this capability built in. There is no program in any standard OS that accepts data over modulated high-frequency sounds received by speakers ... except possibly things like Dolby/DTS decoders for audio. Maybe, just maybe there's an exploit there waiting to happen.
So while malware (or any other program) could communicate with another system using this technique, it's really unlikely that it could spread using this technique. I don't think consumer grade laptop mics are capable of it anyway.