You certainly can, in the game. I had a villain once with a feat called Battering Blow that let you bull rush opponents with your whip. Sure, you can't logically deliver enough force with a whip to send someone flying 20 ft., but it sure looks cool.
It sounds a bit more like a large flail, actually. A flail is a chained weapon that can be used to grab things, but that has a heavy head, whereas a whip is a leather weapon that can be used to grab things, and can only really hurt someone if you crack it, cutting flesh with the tip. I suppose you could just whirl a whip overhead and smack someone in the face with it, but that'd be like hitting someone in the face with a rope. You'd have to swing it very hard to do any damage. I'd say, with a normal whip, that would only do 1 damage plus Str. A small whip would deal a base of 0 damage, plus Str.
Actually, in my mind, a proficient whip wielder ought to be able to hurt people in more ways than just cracking their skin. You could wrap the whip around someone's arm and yank, straining the joint. You could toss things at them with the whip (I read an account of Australian cowboys who can use whips to pluck lizards off the ground, then snap them in half while they're in the air). You could strangle them.
I really don't see why, if a shuriken is able to deal damage to someone in full plate, why a whip can't. Whips can tear through the hide of cows, so it should do more than just bruise an unarmored human. Whips should do lethal damage against unarmored foes, and nonlethal to everyone else.