Yes, because you would be understood but "none" is not a good answer and "no one" is just okay. The best answer is "no". "None" is typically used to answer a question about number or quantity. If the question was "How many students are in the classroom?", you would answer "none" to be correct. "No one" or "nobody" would be a good answer if the question asked was "Who is in the classroom?" when there is nobody there.

You would say "No one is in the classroom." You could use "none" to say something like "None of the students are listening to the teacher."

'None' would be used for saying there's a lack of something. 'No one' is more specifically referring to people. So if you were talking about, for example, chairs, then you could say "There are none in the classroom". Or as said above if you were talking about students (if the topic was clear i.e. - the listener knows you are specifically referring to students) you could also use none. In response to 'Is there anyone in the classroom?', it would be 'There is no one in the classroom'. Sorry, I don't think this was a very clear explanation. >.<'