No. No it won't kill World of Warcraft.
On release day, thousands, maybe millions of people will buy it. It's a big franchise.
On release day, it will be buggy, BioWare won't have anticipated the server load, there will be lag, massive lag. A large proportion of people will either give up then, or go back to Warcraft.
Over the next few days, power levellers will outrun the content because BioWare (caring about the story! THE STORY DAMMIT!!) didn't expect them to level that fast. A decent sized number of them will get bored and wander off. Many of these will go back to Warcraft.
EDIT - Oops, I forgot a vital step! Over these tentative first few weeks, BioWare will patch the arse off of it. Force Lightning will go from the best ability in the game to worthless crap. Everyone that took wrist-mounted flamers will spend their cash on a respec and quit, dissolusioned that this game could ever get out of open beta.
Over the next few weeks, the realisation will dawn that the game is pretty much just World of Warcraft, just with the USP of full dialogue. This will make people feel special... Until they start finding other players who look exactly the same as them. This isn't huge, but it'll put off some people. Some of these will go back to Warcraft, where at least they've got used to looking like everyone else...
Eventually, people will get to the endgame, whereupon they will realise that it's nowhere near as huge, polished or good as Warcraft. Some will start alts and begin the cycle again. Others will leave, because Cataclysm/ANY other game just looks so damn shiney.
This is the timeline of all MMORPGs nowadays.
This being BioWare and Star Wars, it won't die out. Over the next twelve months, it will get a small but gradually growing actual player base. For every five people who try to join, four will be labelled "NOOB!" by the twats who think being max level means they've suddenly mastered the game, and one will find a small council of elite Jedi who will tutor them in the ways of the Old Republic, and who will in time become max level themselves, hopefully to be one of the elite council. The twats will get bored of constant PvP or Raids (plase god don't put raids in The Old Republic...), and many will probably go back to Warcraft, where they at least know the old dungeons.
So it is written, so shall it be.