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Magnetized Liner Inertial Fusion (MagLIF) is a z-pinch magneto-inertial-fusion (MIF) concept studied on the Z Machine at Sandia National Laboratories. Two important metrics characterizing current delivery to a z-pinch load are the peak current and the current-rise time, which is roughly the time interval to reach peak current. It is known that, when driving a z-pinch load with a longer current-rise time, the performance of the z-pinch decreases. However, a theory to understand and quantify this effect is still lacking. In this paper, we utilize a framework based on similarity scaling to analytically investigate the variations in performance of MagLIF loads when varying the current-rise time, or equivalently, the implosion timescale. To maintain similarity between the implosions, we provide the scaling prescriptions of the experimental input parameters defining a MagLIF load and derive the scaling laws for the stagnation conditions and for various performance metrics. We compare predictions of the theory to 2D numerical simulations using the radiation, magneto-hydrodynamic code HYDRA. For several metrics, we find acceptable agreement between the theory and simulations. Our results show that the voltage near the MagLIF load follows a weak scaling law $\smash{φ_{\rm load} \propto t_φ^{-0.12}}$ with respect to the characteristic timescale $t_φ$ of the voltage source, instead of the ideal $\smash{φ_{\rm load} \propto t_φ^{-1}}$ scaling. This occurs because the imploding height of the MagLIF load must increase to preserve end losses. As a consequence of the longer imploding liners, the required total laser preheat energy and delivered electric energy increase. Overall, this study may help understand the trade-offs of the MagLIF design space when considering future pulsed-power generators with shorter and longer current-rise times.