We discuss the design of sampled-data economic nonlinear model predictive control schemes for continuous-time systems. We present novel sufficient convergence conditions that do not require any kind of terminal constraints nor terminal penalties. Instead, the proposed convergence conditions are based on an exact turnpike property of the underlying optimal control problem. We prove that, in the presence of state constraints, the existence of an exact turnpike implies recursive feasibility of the optimization. We draw upon the example of optimal fish harvest to illustrate our findings.