This is an interesting question as it is not entirely clear from the Government Guidance. The Scheme is capable of applying to employees on "any type of contract" so, on the face of it, this would potentially extend to directors where a director is an employee. The potential issue is that the duties of a director will still continue. If the employment contract is in respect of undertaking those duties, it may be difficult to put a director into furlough. Moreover, the guidance states that "an employee can not undertake work for or on behalf of the organisation", which a director will potentially be doing in undertaking his or her duties as a director (whether those duties are undertaken under an employment contract or not).
In truth, it is difficult to give a definite answer. The proof of the pudding may be in the eating, ie making an application may give you your answer.