I see the optical drives (a very geeky name) being called "burners" instead at Dell and many people call the thumb drives "sticks". I'm not saying people don't use the "drive" terminology just that it is on its way out. Laptops have been outselling desktops for several years, and thin/light ones don't have burners. iPads have been a phenomenal success.
Many people already don't distinguish between transient (RAM) and permanent (HD/Flash) memory. (And that distinction is only something that developers should have to care about anyway.)
So while some people may be aware of drives, it will increasingly go the other way.
An optical drive is not necessarily a burner. A burner is capable of writing as well as reading. However, this is borderline irrelevant. Users still know what a CD-ROM drive is. They know what a thumb drive is. Knowing one term (usb stick) doesn't mean they don't know the other (thumb drive). People didn't forget the term "automobile" just because "car" became more popular.
As for laptops, the loss of the optical drive on thin ones is very recent, dating basically to the MacBook Air. iPads are utterly irrelevant. Have people also forgotten what keyboards and mice are since iPads started selling?
You might be right that people will eventually stop using the term drive as its currently used, but right now it's a term with plenty of recognition. And over a longer period of time, rather than the term disappearing, I see no reason why the definition wouldn't simply adapt to refer to online "drives" if physical drives truly died out.
Many people already don't distinguish between transient (RAM) and permanent (HD/Flash) memory. (And that distinction is only something that developers should have to care about anyway.)
So while some people may be aware of drives, it will increasingly go the other way.