No, no it doesn't. Apps in the background get closed as the kernel requires RAM. Almost all Apps go into a "frozen" state when they are not the active application. In this state they consume memory but ZERO cpu resources.
The only backgrounded Apps which continue to run are those that instruct the kernel that they need to, Eg. a music App keeps playing in the background, or Chrome keeps loading a webpage in the background.
Even these Apps that do stuff which uses CPU resources in the background mostly do it by running a very lightweight service in the background, not the full App.
To repeat, the vast majority of apps do not (and in fact are not coded to) use CPU resources when not the active application.
The only thing you are right about is that this allows poorly coded applications to chew through CPU and battery in the background if the developer specifically codes them too. The upside is that it allows developers much more freedom in what they can have their programs do.
Apple decided not to give developers this flexibility for the most part and does not allow apps to run in the background.
And this is why iOS performs better. I like that iOS doesn't allow apps to run in the background, when I want to run an app I will run it. I miss the freedom of Android but not the choppiness, poor battery, bugs etc.
Yes. I forgot about processes using ram resources also. There are a lot more services running intensively in the background than one would think with Android though. Push services, and services to widgets will hinder performance a good amount for example. And system processes always seem to run heavy in background. IMO it seems like the core Android system is written poorly, if it's built in task management wasn't so aggressive, things may run a little smoother.