In simultaneous speech translation (SimulST), finding the best trade-off between high output quality and low latency is a challenging task. To meet the latency constraints posed by different application scenarios, multiple dedicated SimulST models are usually trained and maintained, generating high computational costs. In this paper, also motivated by the increased sensitivity towards sustainable AI, we investigate whether a single model trained offline can serve both offline and simultaneous applications under different latency regimes without additional training or adaptation. Experiments on en→{de, es} show that, aside from facilitating the adoption of well-established offline architectures and training strategies without affecting latency, the offline solution achieves similar or better quality compared to the standard SimulST training protocol, also being competitive with the state-of-the-art system.