No, that is not how it works. The "multitasking dock" is really just a "recently used apps dock." Just because an app appears there doesn't mean it is consuming processing power or battery. There is no need to manually close apps from there in order to conserve resources. The OS handles it intelligently.
If you open the app that is currently in the dock (pressing twice the home button) it will resume from where it was. If you quit it in the dock and then open the app it will restart from the begin. I assume it's "multitasking".