I don't see why not. I'll be curious to hear how that works out!
Lorewise I don't see why not, vampires are predatory by nature so turning on their own kind would be entirely in character if there was an advantage to be gained by it.
I believe joining the Dawnguard is precluded by being a vampire, not sure about becoming one after recruitment though
Joining is not the problem. Everybody just acts like he don't recognize the player as a vampire.
In the Dawnguard-Line, there is one point where you are tested to be a vampire. You have to cure yourself if the story should go on.
You also get the famous follower Serana. She will offer to turn you into a vampire from one point on.
You can start Dawnguard questiline even if you are a vampire and you can complete the first quest, but if you wanna continue to receive quests from Dawnguard, you'll have to cure yourself.
https://www.youtube.com/watch?v=P8Znn-4dxQ0
There are many reasons a vampire may want to take out other vampires. Too many vampires results in too many vampire hunters and angry mobs. In Oblivion, there is a quest where one very prominent vampire (most of you know who, but just in case there is that one guy who doesn't, I won't spoil) tasks you to get rid of a den of vampires in his territory.
And with Dawnguard, you can pretty much go back and forth between being a vampire and a mortal at will. Warning, though ... becoming a vampire will cure being a werewolf, and you can only become a werewolf twice ever.