Except that Vanilla includes the Forsaken as a faction, Rexxar as the champion of the Horde, Theramore no longer allied with Orgrimmar, and references to Illidan's defeat and Arthas as the Lich King.
Beyond that, we know that the night elf, blood elf, and undead campaigns had to have happened over a short span of time, because Illidan's actions in the former cracked the Frozen Throne and the Lich King's power was draining quickly enough that Arthas had to literally drop everything and book it to Northrend in order to make it there in time. From the end of the night elf campaign to the end of the undead campaign would have been measured in weeks--months, at most. No way it would have been four years.
So exactly what TFT storylines could possibly be happening concurrently with vanilla WoW?