If I quest now in World of Warcraft, will I have the exp gained when I buy Wrath of the Lich King?

Okay, so I am a huge WoW player. Right now, I have a level 70 Tauren warrior and level 48 Troll druid. I have BC, but not WotLK. However, I'm going to buy WotLK within the next few days. I really want to go to the Caverns of Time in Tanaris to quest, but I'm afraid the exp will just be thrown away, since I don't have WotLK to level up past 70. So here's my question: If I quest now, will the gained exp show up when I buy WotLK?