This is possible if you would change the background image in your custom stylesheet and put it in the right top corner.
Example:
.tundra .mendixDialog_error .mendixDialog_content {
background: url(images/layout/bg_error.gif) no-repeat right top; }
Class warning pop up: mendixDialog_warning Class information pop up: mendixDialog_message
It's not possible to add HTML/text to the pop up.
Yes, you could change the background with an image. Open firebug and identify the correct css class. I've found the css class for the warning:
.tundra .mendixDialog_warning