Yes the corrosion on the battery terminals and battery post can cause the electrical system to lose connection which would result in the cars starter not engaging or just clicking.
The battery terminals and battery posts being corroded can also interfere with the electrical connection and not allow the alternator to charge the vehicles battery back up when driving down the road.
That can then lead to a dead battery and a car that won't start.
You can pour some baking soda and water over the battery terminals and battery posts to get rid of the corrosion on the battery and then wash it off with a hose.
If the vehicle still doesn't start then make sure the battery is up by either jumping it or charging it with a battery charger.
Another good idea is to remove the battery terminals from the battery and clean the battery terminals and battery posts with a battery post and terminal cleaner that you can get at any auto parts store for fairly cheap.