As someone else in another thread summarized it nicely: if you'd say "nem van", use "nincs" instead.
I am auditing my Hungarian grammar here. But have stayed in this country long enough to converse in it. This one is delivered like a query. Not only as an exclamation. Also I checked it with my Hungarian husband and the intonation can also be taken as a query. "Is it Eva who is not well?"
Cool. Good to know. It doesn't sound like a question at all to me, but I don't know quite how Hungarian question intonation sounds.