I'm not worried about stopping it, and the one experience has been two vampire thralls in Dawnstar, one of which was apparently killed easily before I ever noticed, the second one, dispatched easily by the town guard while I was standing there.
I just want to know if they are going to escalate if I officially start the quest.
Okay, if I understand you correctly, you're asking about vampire attacks before and after you start the Dawnguard questline. I've played through the questline one and a half-times, and I have a character who has not started the quest (but is Level 30).
Frankly, I haven't seen a lot of difference in the attacks before and after starting the DG quest. Obviously, if you finish it they seem to go away. They seem to "escalate" regardless of whether or not you start the quest. At higher levels, there is usually one master vampire with two thralls, and with my level 30 character, if I don't stop what I'm doing and kill the master vampire, it'll take out one or more NPCs. Since they hit in cities, that can include some trainers and merchants you might need later. So be on your toes!
For some people, this is such a problem that they uncheck DG in the load order and keep it off until they're ready to start the quest. From what I gather, if you fast travel into the cities, it's much worse. Since I rarely fast travel into cities (if I have to FT, I take my horse and travel to the stables outside of town), I haven't noticed a significant problem.
I hope that helps (and without too manys spoilers).