At high Reynolds numbers the flow will be fully turbulent.

In general flows vary very little with changes in Reynolds number until they reach a critical value when they change quite abruptly from laminar to turbulent flows.

Below this critical point they change little and above this critical point they change little.

Reynolds number gives a measure of where this critical point will be for the flow you are considering.

Provided all your flow is above this critical value (which is almost a certainty for flow in a pipe), then the loss coefficient will not vary significantly with Reynolds number.