Widgets don't actually "run" themselves, like normal apps do. The widget host (i.e. the home screen app, or the lock screen) is in charge of drawing all the widgets. The widget provider (part of the app) tells the host what layout to give each widget, and how often it wants the widget to update. There's nothing running to "suspend", regardless of whether the widget is visible or not.
The interface that widget providers use to specify what the layout should be allows them to give a list of things to rotate through. The YouTube widget uses this, for example, so that the widget can keep showing new videos without the provider having to keep changing the layout. If your widget uses this facility, then the home screen only runs any extra code when it's time to rotate the list.
Of course, it's also possible for a background service to keep giving the host (home screen) a new layout for the widget. This is how (say) an email widget can be updated when you have new emails. But there's no need for it to run all the time to do this, and having a rotating list shouldn't in itself make you think the app is always running in the background.