No! Chickens lay quite happily without the amorous intentions of a handsome red wattled male, such as old Perky here.
Should you have a cockerel, you can be sure he will do his best to fertilise the eggs. If a chicken is broody she will then sit on these eggs for 21 days (the incubation period) and with a bit of luck these eggs will hatch and produce more chickens.
The eggs a chicken lays without the help of a cockerel are not fertilised and will therefore never hatch.