Yes corrosion can prevent a car from starting because the corrosion can prevent the battery terminals from making a good connection from the battery to the alternator or starter.
When the starter doesn't get a good connection then the car will not be able to start and the starter will likely click or not do anything at all.
If your battery terminals are corroded remove the battery terminal connections and clean them up really good using a battery terminal cleaning tool or brush.
You can also remove corrosion safely from vehicle battery terminals by mixing some baking soda and water together and pouring it on the vehicles battery terminals and let it sit for 20 to 30 minutes to remove the corrosion.
Then just use a garden hose and rinse the battery terminals off with the water.
It's best to remove the battery connections and clean those up really good because the battery could be undercharging due to bad connections from the alternator to the battery.