No. IMO the Voyager, iQube and (properly working)Diablo trounce the crap out of a Hornet. A PRII is still one of my favorites, but you run into the size issue, as you do with the LisaIII.
As far as the smaller amps go, I think a GoVibe Petite and GoVibe Magnum trounce a Hornet as well. I think the amp name carries it's past of a "good amp, but not great" aura, but since it's been picked up by Uncle Wilson, I think it's quite the opposite and are now formidable amps. No, the can't drive fullsize cans, but honestly, What are you doing trying to drive K701's with a tiny amp????
Yeah, it's an amp, but that's like me asking you to tow a boat with a Geo Metro. Sure, it's a vehicle and can haul crap, but it's not exactly the application it was intended for. You're asking WAYYYY too much for something so small to do.