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Unfortunately you've got the wrong idea here. It'll help to not think of Android like a desktop computer. Your Homescreen is not a desktop, it is a place to access often used apps or widgets for apps. Apps do not run on the homescreen, it is an app itself. There isn't really a way to switch from app to app like alt-tab or something without a 3rd party app. Apps do continue running in the background until you or the system stop it, you just launch the app again pick up where you left off.
The quick answer to your question then is no. There is an app that has potential as a good app switcher called Visual Task Switcher. It's not perfect, but it could be good with some work.