I had Dead Money, Honest Hearts, and Old World Blues installed, way back when I had to re-install Fallout: New Vegas and never bothered to re-download the Classic Pack (Vault 13) I had gotten as a pre-order. As I was creating a new character I had remembered the pack, so I quit out of the game and downloaded/installed it. Upon going back into the game, I at least no longer had access to the Traits available for purchasing Old World Blues, and did not get any indication that any of the DLC had loaded through in-game pop-up windows while in the world.
I haven't looked further than that into it, as I am now re-downloading and installing all the DLCs just to err on the side of caution. I had also been updated to the latest patch.