The El Niño-Southern Oscillation, or ENSO, manifests itself as periodic fluctuations in sea surface temperature and atmospheric conditions across the equatorial Pacific Ocean, which are notoriously hard to predict even with sophisticated global climate models. This motivates simpler representations of ENSO by considering the underlying feedback mechanisms only. We are interested in delay differential equation (DDE) models for ENSO, that portray the interaction between delayed feedback and seasonal forcing. In such conceptual climate models, delayed processes are generally assumed to be constant. However, it is important to note that the use of constant delays is a modelling assumption. Delays in climate models are inherently non-constant and depend on the state of the system, and this makes state-dependence an appealing consideration from a modelling perspective. We study here an ENSO DDE model where the delayed negative feedback is modelled by a step function. This enables us to prove that, for a large range of parameters, implicit state-dependent delay does not give different dynamics compared to the constant-delay case. These findings provide insight into why a single feedback term with implicit time delay may not significantly affect the dynamics, as was observed in a prior investigation.