Yes an exhaust manifold leak can cause loss of engine power and negatively affect engine performance.
An exhaust manifold leak can also cause burned exhaust valves as well as an improper fuel trim as the leak introduces extra oxygen that is picked up by the oxygen sensor.
When an exhaust manifold leaks between the engine and the exhaust manifold it introduces excess oxygen that the oxygen sensor picks up so it can increase your fuel consumption as well.
If possible get the exhaust manifold leak fixed as soon as possible so that you don't lose the engine power or have engine performance issues.
Your vehicles engine will also sound quieter as well when you replace the exhaust manifold gaskets.