An intake manifold gasket leak can cause rough idle but the exhaust manifold leaking shouldn't cause a rough idle on your vehicle.
However exhaust manifold leaks can affect your engines performance and cause things such as loss of engine power, poor acceleration, decrease in fuel efficiency and even cause a burning smell to come from the engine bay.
If you do have an exhaust manifold leak it really should be fixed so it doesn't mess with the vehicles engine performance will also quiet the vehicles engine down.
When the exhaust is leaking it doesn't allow the engine to have the proper air pressures inside it to keep the engine running correctly which important.
A bad EGR valve or clogged or dirty fuel injectors could cause the rough idle or a bad idle air control valve.
But the exhaust manifold leak shouldn't be a cause of the rough idle.