I am using pictures with different sizes for the desktop and the mobile version of the web, and I want to know if checking “Hide this Stack” to hide a picture on the mobile version still loads it and therefore I should be using the same picture for the desktop and mobile versions of the page.
Yes - it still loads the stack. Checking the box creates exceptions in the CSS that either show or hide the content depending on the size of the viewable window. So, for example, if the viewable size of a window gets below a certain width in pixels, the CSS will tell the browser not to show one element, but another instead. If the visitor increases the window width, the reverse happens. In the background though, all elements for both scenarios are loaded into RAM.
If you REALLY don’t want content to load in certain instances, you can make loading conditional on the user agent string that the browser sends along with HTTP requests - so if the browsers tells the server that they’re “Mobile Safari”, the server only sends the content over the line that is applicable for that browser’s user agent.
You can do this using some coding, but if you like a drag and drop solution, the Agent stack ($40, Weaver’s Space) allows you to set this up without any coding.