No, he won’t get the 2004 questing experience. The expansion Cataclysm revamped all the questing zones on Azeroth, so he would be questing through the time immediately following Deathwing’s emergence and all the destruction rained upon the planet.
If he wants the true 2004 questing experience, he’d want to play Classic WoW, though I don’t recommend leveling a Classic character unless he’s willing to be patient, doesn’t mind a little grinding, and can have fun with a much, much slower journey to 60.
If he wants to dive into an immersive, lore-focused experience, then I recommend he pick out a race that appeals to him and level through an expansion that also appeals to him. The lore of Azeroth is absolutely enormous, there’s no way to take it all in chronologically, and most zone questlines are self-contained enough that players with little knowledge of the lore can still learn a lot and enjoy the story.
Here’s my favorite zones to quest through for each expansion when it comes to cool quests/lore or they’re just pretty and immersive. Bolded are my top choices.
Azeroth/Cataclysm - Silverpine Forest, Redridge Mountains, Un’goro Crater, Duskwood, Ghostlands, Twilight Highlands, Mount Hyjal
Burning Crusade - Zangarmarsh, Nagrand, Netherstorm
Wrath of the Lich King - Dragonblight, Zul’drak, Howling Fjord
Mists of Pandaria - Valley of the Four Winds, Jade Forest
Draenor- Gorgrond, Shadowmoon Valley, Talador
Legion - Val’sharah, Azsuna, Suramar
BfA - Drustvar, Nazmir
I’d say Suramar is one of the absolute best questlines in the game. It’s very long, and Suramar can be tedious to navigate without flying, but it’s worth it. Great characters and compelling stakes.
I’d recommend Legion to start with just in general, as each zone has a little something for just about any player regardless of what element of the lore they might be interested in, and I’d confidently argue that Legion has the strongest writing and least monotonous questing experience over every other expansion.