The legislation states that the temporary councillors serve "until other councillors are elected" so, in theory, yes. This would depend upon the wording of the resolution of the District Council.
There is an assumption within much of the legislation relating to parish councils that communities are full of people who care enough to put themselves forward for community leadership roles. That may well have been the case in 1972, however the same may not be true as we drift through the 21st century. All three of my parish councils, although quorate, will start the new year seeking to co-opt new members to fill the vacancies created by insufficient nominations for the forthcoming election.