Yes they will. A hen will lay eggs whether a rooster is present or not.
In fact, there is very little reason to have a rooster around if you only keep a handful of chickens for eggs. We would advise against it unless you have more than 6 hens, then maybe there is more of a reason to have one. Obviously if you want baby chicks then you must have a rooster with your hens to fertilise their eggs.
Your hens will produce eggs hopefully on a regular basis and their production won’t increase or decrease because you have or don’t have a rooster about. So in the back garden, hobbyist world they serve little purpose!