The answer to this first question is both yes and no. By that I mean, this isn't an either/or question. The artists of the Neo-Classical period were in fact inspired by the Greeks and Romans…as they understood them, filtered through their own eyes. Some elements of this art show direct and clear influences from the Classical period. The emphasis on clean lines in representations of human anatomy, and, more obviously, the use of stylized columns, show direct inspiration.
However, the uniqueness of these works comes from the incorporation of NEO-classical values, and, to be frank, misunderstandings of the period. An easy example here would be the relative rigidity of design and relative lack of emotion in Neo-Classical work; this shows a misreading of classical works.