I would not say that at all. Most computers that I have disassembled have a much smaller piezoelectric speaker for the post beep, and a seperate paper cone speaker for audio, like the ones you show in your pics.
I have driven similar speakers with a BUF634 to uncomfortably loud levels. You shouldn't expect it to sound like nice monitors, but it will work. I still have one on the bench for occasional testing and whatnot.
You should keep them for a future experiment when it pops into your head.
I happen to like paper much better than plastic when it comes to headphone drivers.










