Ghostcrawler has recently confirmed, via Twitter, that the Siege of Orgrimmar normal mode will be completely open the first week of the new patch.
@giraffejerry The plan is normal will all open on the first week.- Greg Street (@Ghostcrawler) August 30, 2013
Or at least that is, as he says, "the plan", and as we all know, plans can change! As twitterati chou explained in his question, there seemed to have been some confusion about the availability of the different wings of the Siege of Orgrimmar at launch. Let's hope this clears all that up. You could potentially even kill Garrosh that very first week! ...If you're prepared enough!