The long answer is Yes, it can be done, however this is not the standard way in which ClassiPress works, so effectively you would need to do some customization to the theme to achieve what you are asking. As it is as the moment, the most you could do from the ClassiPress admin dashboard is make your ads free, and restrict buyers from using the sidebar contact form unless they are registered users, however there is no subscription package or page restrictions in place.
If you are not planning to do the customization yourself, we have a
certified partners page where you can find recommended coders for hire who may be able to give you an idea of what is involved/price.