We investigate data-driven surrogates for parametric, time-dependent PDEs based on Deep Orthogonal Decomposition (DOD). On the theory side, we extend the data-driven POD-based ROM arguments to the DOD setting and identify a quantitative dependence of the online performance on the regularity of an associated optimal map. Furthermore, we show the specific requirements of problem size and desired error tolerance to assert superiority of DOD-based ROM efficiency above POD-based ROMs. Computationally, we implement a side-by-side comparison with a POD reduction baseline. This work extends recent advances in data-driven model order reduction and neural network?based ROMs to the continuously adaptive DOD framework.