Whoopsa, you're right. I tend to forget that nincs already contains van.

It does make sense, yes, but the grammar seems off to me. If you go for nonexistance, you usually use "There is no [noun]." There is no knife in the kitchen. There are no fish in the river. There is no joy in my life. Or perhaps with "There isn't any [noun]". But "There isn't a [noun]" sounds strange.

Perhaps the reason is that "not" is an adverb, and "to be" has a pretty hard time with adverbs. If you start with "There is not a roof on the house", I kinda expect you to follow with "but an airship". Like, what is on the house instead. It sounds like "A házon nem tető van."