It's entirely possible for a HG to leak this much, but before taking the head off I would make 100% sure it is not coming from somewhere else, can't see there being a core plug at the front, they are normally in the rear and sides to let the gasses out when being cast, nothing to do with protecting the engine if it freezes.
It could be the water pump itself leaking past the seals, a lot have a hole in the underside that lets water out if it gets past the inner most seal.
If you sprinkle talcum powder around any water loss will remove the powder and show you where it's from, cheap and easy.
tabetha