Not directly, but they'll improve the fitness of your chest/shoulders/back muscles that are also used for bench to varying degrees and improve your endurance. This will likely help you get a better workout in when you do the bench press which will then lead to heavier weight.
Maybe if you're just starting lifting or if you're pretty fat. Push-ups are high rep low weight more akin to cardio than bench presses. You can do weighted pushups as others have mentioned though.
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