When you upgrade the WoW free trial off of WoW's website (using the upgrade online method) does anyone know if the Burning Crusade will run, or should I buy the real game for a CD key?
The online upgrade is the same as going and buying a real copy of the game. The only difference between the trial and the full game is that the serial key they give you for full game upgrade (or store bought full game) unlocks the limits they put on your trial account.
You won't have any trouble installing burning crusade when it comes out.