Yes, this is by design. When the CssFiles property is set the editor stops to pick up the styles from the page where it resides.
In your scenario you should manually add the .VerdanaFont10Line15 class to the ~/css/EditorContentArea.css file and the class will be applied to the content area through the CssFiles property.
The other approach is to set the content area appearance via the ContentAreaCssFile="~/css/EditorContentArea.css" property. Therefore the editor will continue to apply the styles from the page to its content area.
the Telerik team