Unless the discs are from the latest expansion, they are useless.
The game only needs to download about 1% of the total game to become playable.
I have done download installs over very slow connections.
The game will install the game engine and other core content that it needs to function at all. Then it will activate the "Play" button. As you make choices it "on the fly" downloads needed content. A small load bar shows what it's doing.
For instance as you create a new character, it will balk for a few seconds to load something. The initial "enter world" screen will take a solid couple of minutes. NPCs and objects will render funny for a few seconds while it loads their visuals. Very soon, the areas settles down and feels like normal play. It works better than you think.
Well it's designed to work even faster, to be almost unobtrusive, but our connections are slow.
You can mess with it; hop on a flying mount and you will laughably overtake its ability to download content. It wireframes the terrain well enough you can recognize where you are and avoid flying into terrain. Suddenly land in a never-seen zone and expect to be attacked by invisible monsters. Cure this by circling the area low while it renders.
Busy cities like Dalaran are also a challenge to load initially due to the hundreds of player characters, each with unique armor/weapons. If loading a character that's in-town, I recommend getting out of town ASAP, tilt camera at your feet or sky to reduce number of characters in view.
Once you get to a destination and get down to business, it stabilizes quickly.