The Chatbot component, MIT provides a certain amount of 'free' usage by paying chatgpt it's fees. The free usage subsidized by MIT is shared by all the Chatbot component users and is limited When the 'free' usage for demonstration purposes is used up for the month, the component will throw an error saying it's allocation is used up. This happens usually during the end of the month as users gobble up the limit set by MIT but can occur sooner in the month if the feature is heavily used.. MIT usually resets the limit at the beginning of the month.
I doubt no key usage will work successfully for all your students with the amount of usage you contemplate. I asked one of the MIT staff to comment here so look for MIT's comments and they can explain in detail.