Hardware-implemented reservoir computing (RC) has been gaining considerable interest in recent years, in particular for classification and nonlinear-prediction tasks. Such RC systems often perform analog computation and, therefore, may be more sensitive to noise than digital systems; noise has been found to often degrade the computational performance. In contrast, here we demonstrate that noise can also play a constructive role in hardware-based RC. Using a hybrid delay-based RC system with an analog part (nonlinearity) and a digital part, we show that the replication of chaotic attractor dynamics is overall improved when the reservoir is trained with an input signal modified by additive Gaussian noise. To quantify the performance of the attractor replication, we suggest two different methods based on recurrence plots and power spectra.