Indeed, “se dilater la rate”, for some reason, means laughing, “ça me dilate la rate” = cela me fait rire. But it’s quite uncommon (perhaps it used to be more so when Goscinny was writing)
I don’t think there’s a pun with Harun el Poussah. A “poussah” is a fat man. Not much used, either. Harun el Poussah is simply Harun the Fat.