I think you've answered your own question. The handout is clearly referring to the detergent case, and the detergent is the key issue here, not the polyacrylamide.
Detergents work by coating the proteins uniformly with negatively charged molecules.
Separation can only be based on size. 1a and 1b of the appropriate section in the Sickle Cell website also make this distinction. I can't think of an electrophoresis application that doesn't use a gel. You may get to play with the stuff if you take Lab on DNA Manipulation. However, you're thinking that it would be ironic and the fact that it's not IS ironic.