The FAQ does say that you can use PokéBank/Transporter as soon as you get the Pokédex, but it goes on to say that there are some Pokémon that cannot be stored or transferred. They're probably talking about event legendaries, like the Nasty Plot Celebi and the shiny Beast trio needing the Relocator in BW1 to be transferred from DPtHGSS, but
the new PokéBank website isn't telling which ones will have such restrictions. Instead, it advises you to test for yourself which ones can and cannot be transferred. Chances are, though, that you'll be able to transfer story legendaries, like the Sinnoh dragons, Lugia, Ho-oh, the Unova dragons, etc., without restrictions. Whether or not you can control them, however, is up to your current badge count.
Also, it's entirely possible to clear the main scenario in just two days, so eight days (I'm not sure why you said month, the service goes live next Friday) is plenty of time to beat the game. That's not to say you'll need to rush it, because you certainly don't! You can take your time and enjoy X/Y as long as you like, your Pokémon will be transferrable as soon as you choose your starter and receive the Pokédex.