Aha, I think I have an answer for this now, after consulting my brother who has always been a computer person. I really wasn't, maybe a few game, until the internet really got big.
He said the technology for the internet techically existed since 1969, but of course wasn't known or used by the general public. What Al Gore really said about him and the internet is that he backed crucial legislation that facilitated the internet technology being made available to the general public, because before that it was just for the gov't and Dept. of Defense, maybe a few big corporations.
He told me that as early as 1984, a form of email could be sent using UNIX (whatever that is/was) and services like Genie and CompuServe. These were the forerunners of AOL, which did not come about until the early 90's. Colleges used email in the mid-late 80's, and students with computers in rooms had access to it (he went to college, I didn't) As I said before, and he verified, it was not common or easy to use computers back then for things other than video games. You really had to know something about what you were doing, so only the most knowledgeable 'geeks' (he is a self confessed computer 'geek') even bothered to mess with them. They were mostly teenage boys and college students, or people who worked with computers in their job, or- one more group of people had access and frequently used it- RICH PEOPLE!! I asked if he thought Edge would have had it, and he said, "The Edge? Yes! Definitely!"
He was rich, and with the band on tour such things were useful. Of course, U2 was ahead of their time, and Edge is a computer guy, so it all adds up. I think the case is solved, yes, it existed (though not like you see it today) and Edge, you had mail