There are some circumstances where calibration would not be needed. However, they are relatively few. They also require the pH meter to be working correctly. If the meter can't be standardized, there is a moderate chance it isn't working. That functioning meter problem needs to be addressed first.
If you are titrating to a specific pH as an endpoint, then the calibration of the pH meter is critical. Likewise, if you are titrating a multiprotic acid (say phosphoric acid), you need to know which form of the acid you are titrating.
One exception would be a potentiometric titration where you are measuring mv vs ml of titrant. You need to know what form of acid you are titrating. From this information, you could plot out the curve and determine the endpoint without knowing the exact value of pH. Say, using a first derivative plot on semilog paper.