Nothing is impossible 
but it does come down to “Is it worth the risk for the DAO?”
The balance sheet lies in the legal entity, which is a Foundation. In theory of course it is possible that the DAO could vote to convert APE into ETH - the Foundation entity could hold other assets than APE (again, in theory). However, there is a clear preference at this time for the direction of the DAO to be only granting out APE, therefore, I doubt it would hold up to Special Council review.