Do you want to appoint a new strata manager or renew the contract of the existing one?
I’m not familiar with the Act, one way of looking at it is in terms of whether the EC can renew without GM approval is whether any other strata manager has been proposed. If there has, then it would have to be put to a GM vote. Also as the strata manager is usually appointed at the GM, the contract would usually come up for renewal at the time of the next GM, so there is no problem with putting it to the GM for approval.
In terms of poll votes, if someone calls for a poll then the votes are determined by poll, i.e. by lot entitlement, as distinct by voting on a show of hands. You can’t stop that if someone asks for a resolution to be determined by poll.
I am not sure if you are asking if the EC could renew the appointment and then someone moves to rescind the appointment at the GM. If the motion to rescind succeeded on a poll then theoretically yes, but it would be difficult if the contract with the SM had already been signed, as on its face it would be a legally binding contract. I don’t think you would want to get into such a messy situation.