No, they do not drain the battery. We don't have it on the iPad unless there is an app that does it but on my Droid I have a battery usage meter that shows what is using how much percentage of the battery drain. Apps running in the background rarely show up, if they do it's 2%. Not a big drain at all.
So if you multitask with 4.2.1 you will have an app running in the background, but after a while if you don't return to it the OS will completely shut it down. This is nothing for people do be concerned about. I just noticed that some are so that's why I was talking about it.