You can, it is quite correct. There is nothing wrong with this sentence. However, native speakers tend not to use this form very often in conversation. In informal situations, we are more likely to say: There are a lot of students. Perhaps you are confusing this with what you have been told about 'much'. It is true that we very rarely use 'much' in positive sentences. While the sentence 'There is much money' is technically correct, it sounds very old-fashioned and unnatural, and a native English speaker is unlikely ever to say this. In informal contexts we'd say There is a lot of money. Meanwhile in more formal contexts, we'd rephrase as, for example: There is a great deal of money.

You don't have to use many in negatives, many is for contable things and it means a lot. Yes you can say There are many students in the classroom, they are a lot, and if you want to say that they aren't many or in a negative way you can say, "There are few students in the classroom".