As NoiseJockey puts it, sound influences user interfacing and/or user experience, not engineering (which builds up to user interfacing, not the other way around).
I'm not so sure if the given point about manufacturing costs is the reason (or a reason) for using sound messaging in products, although it's arguable that it does happen to be cheaper to implement. But sound messaging is more intuitively understood simply as a more immediate message that doesn't need to be read to understand, which makes it more suitable for simple messages or messages that need immediate response than a LCD.
Depending on the product sound can be an important part of the brand and non-tangible appearance of the product (what does the product feel like, rather than what it is). Few examples include mobile phones and mobile phone application sounds, computer application sounds and car doors.
Which to me begs the question "as audio people, what sounds do we create that have influenced engineering?"
If you'd like to understand this question, I'd advice looking at movies (e.g. scifi) and seeing, whether you find films that have or may have projected some kind of technological inventions and their usage or consequences. That I think is the most direct way to influence engineering and technology development through sound.