Of course, the level 80 titles have been removed, so there's not any real ingame need to rush to level 80, but people will of course do it anyway. Odds are that within the first day after release, we'll see a few level 80s floating around, and I'd imagine that all of the various realms will have at least one or two level 80s within the first few days. The fastest people will do it with the help of their guildies (or saved quest items), but there'll probably be a few people who will just go nuts and get it done all on their own.
I won't be one of them, and I'm sure there are plenty of players like me, who are more interested in seeing the content rather than reaching the next highest level as fast as possible (and that's exactly what Zarhym recommends as well). A few people will race to 80, no question, but the vast majority of people playing will likely be taking their sweet time.