The increasing integration of renewable energy sources has led to a rise in Power Electronics Interfaced Resources (PEIR), challenging traditional Root Mean Square (RMS) based modelling and stability analysis. Unlike synchronous machines, PEIR display fast dynamics across a wide frequency range, necessitating Electromagnetic Transient (EMT) models to capture high-frequency phenomena. Despite this, RMS models are still widely used to study slow system dynamics, even under high PEIR penetration. This study evaluates the adequacy of RMS models for analyzing slow dynamics in converter-dominated systems, focusing on Grid-Following (GFL) control schemes. A generic GFL converter is modeled in EMT and simplified to RMS. State-space analysis reveals that current control, a fast control loop often simplified in RMS models, affects slow modes, challenging the assumption that RMS models accurately capture slow dynamics. Comparative EMT and RMS simulations confirm these initial findings, underscoring the limitations of RMS models and the importance of considering fast control dynamics, even in slow timescale studies.