In short it is highly unlikely. The first step in any investigation is to review the constitution of the SMSF trustee company to determine how a director. is appointed An EPOA has no power to appoint a director - see the ATO EPOA ruling in that regard: SMSFR2010/2
The Commissioner states as follows in para 11:
The legal personal representative performs their duties as a trustee of the SMSF, or a director of the corporate trustee of the SMSF, pursuant to their appointment to that position rather than as an attorney or agent for the member. Consequently, any proscriptions contained in State or Territory legislation against conferring trustee duties and powers via a power of attorney or common law restrictions on attorneys undertaking directors duties are not relevant to the application of the exception contained in subparagraph 17A(3)(b)(ii).
So will an ordinary company constitution enable an EPOA to be appointed as a director of the company? The answer is NO! If the other directors don't want the attorney as a director then they can refuse to appoint them. This may then require a shareholders meeting. So a long, complicated and expensive process from something that should be simple.
The LightYear Docs Solution
Our special purpose corporate trustee provides for a member's enduring attorney to act as their Successor Director. This is completed as a separate section in the EPOA and follows the recent decision in G v G  NSWSC 818 where specifics rather than general powers should be used with SMSF issues.
The solution in the LightYear Docs EPOA provides for a binding director's resolution appointing the attorney as a Successor Director in the event of incapacity, immediately should the member no longer want to act as a director or in the event of death. Once signed other directors cannot prevent the appointment.
More importantly the special purpose constitution limits dealing with a Principal's super (being the member with the EPOA) to the Successor Director only.