From what I can tell, they do.
However, with AppHabor, I can now attach to a specific branch in the repository. When done this way, only changes to that branch cause AppHarbor to get the updates and republish my website.
So I now have 3 "permanent" branches...
- "dev" that I can push to any time and is not monitored by AppHarbor
- "uat" that I pull from "dev" when desired, and this updates my UAT web site
- "live" that I pull from "uat" when desired, and this updates my Live web site