Have played several iterations of Buffy and have not completed the MQ. The farthest we went was hunting for Esbern down in the Ratway. By that time, Buffy had seen several mammoths killed by random dragons and was not at all happy.
So we did some more study on UESPwiki and discovered something that all of you who have been playing a long time likely already know. Random dragon spwans stop while Delphine's 'kill da dragon' quest is active. While that quest is active, they only spawn and hang out at their dragon walls. That point is also far enough along to render the Dragonborn DLC available. Woot! New Game!
Since then, our pattern is to pick up the horn from Delphine, tell her we don't have time for her nonsense and be on our way.
The thing is, Skyrim is a land rich with the lore of dragons and I like having a FEW dragons in the game. And Buffy, with her hefty magic resistance and powerful bow can kill them just fine as long as she can keep her distance (easy to do). Generally, the Graydudes conclude that, although she may carry the spirit of a dragon (Phantom) within her, Buffy does not carry their blood - she is not dragonborn.
Since progressing the MQ further (even completing it) would only mean plenty of random dragon spawns, it is not likely we'll ever complete it. The exception might be an 'out of body' experience to complete it (just out of curiosity) just before restarting the game anew.
Another way to look at it, I suppose, is this: Buffy's only encounter with Alduin is when he saved her life at Helgen. How does that make him a foe?