You can register an ultralight, fat or not, even if it has already flown, as E-AB provided you have the build documentation showing that it was indeed amateur built, and provided that it wasn't so prefabricated by a kit manufacturer that it's just a bolt together assembly (< 51%). AC103-7 talks about this.

You can't register a backpack powered paraglider because the rules now say it must have a landing gear, and they don't mean feet.