But I don't think it will. Even if we ignore the extra cost and the inevitable issues with the reliability of the laptops, there is still the simple fact that computers are not always more convenient than paper!
When I was in school, cramming before an exam, I often took textbooks to the bathroom with me, or I'd read them in the car (while my father drove me to school), or I'd read them outdoors. Now try doing this with a laptop. In the bathroom? Better not let any water from the sink (or elsewhere) splash onto the computer. In the car? Vibration isn't good for hard drives. Outdoors? Hope the battery doesn't go dead.
And, of course, without an internet connection, the computer will only be as useful as what is stored on the hard drive. Can we be certain that every student will have regular access to a broadband connection, in order to download texts? Can the school afford to pay for DSL lines to those households that can't afford them? Dial-up will be barely adequate, as anybody who has attempted to do research over a dial-up connection can testify.
All this assumes that the hardware will be completely reliable. But will it be? Hard drives fail. Laptops have all sorts of problems. If the computers are Windows based, we'll have to worry about virusses and spyware. And if the student's network connection is wireless, we'll have to contend with student breaking into each others' computers.
I'm waiting for the 21st century equivalents of "my dog ate my homework". Maybe "the e-mail got lost", or "my hard drive glitched", or "my finger slipped and I deleted the file by mistake".