Yes, they will either take the money from the deposit they hold on your credit card, get you to pay for it or take the amount from your credit card if you refuse.

You should tell the front desk that you broke it, otherwise, they are going to send an email to you saying that they took the damage deposit from your credit card.

Sometimes it may not be a lot. For example, a friend of mine broke an entire bed once when he fell on it (he is a large man). He thought he had to buy a new bed, nope, just a $10 beam for the bed.

-Madison Mussio