One can discuss scaling of the gradient evaluation time in the context of a given Stan program, but without that Stan program there’s not much one can say. The entirely of Stan’s computation time, however, is not determined by the gradient evaluation time but rather the gradient evaluation time and the number of gradient evaluations needed. The scaling of the number of gradient evaluations needed will depend on the particular data, the assumed model/Stan program, and the provenance of the data.
For some more discussion see Addressing Stan speed claims in general - #45 by emiruz and Chains stuck when use larger dataset, but not smaller.