Yes, you can use "いいえ” to answer that question.
Although "教室の中には椅子はありません。" is gramatically correct; most of Japanese people would not use that expression. Because it sounds quite "systematic" like an answer from a robot. I think that the Japanese tend to answer just "いいえ、ありません。” or "いいえ、椅子はありません。”, or, in casual way, "いいえ、椅子はないですよ。." Though the Japanese textbooks might have demonstrated you to answer it with "ful-sentence" like you mentioned in your question. So If your question is asking whether your dialog is gramatically correct or not, then I would say yes. But if your question is asking whether your expression is common or not, I would say it is not correct.
