Charges for data connectivity can be applied if you are connected to the Internet using mobile data. If you are connected to a WiFi network, no charges will be applied.
How much data is used and charged for, is not easy to say due to that every contact list is different. How much data is used during a sync is depending on how many contacts you have, if this is the first sync or not and if your contacts have profile pictures.
A normal contact list with around 300 contacts takes approximately 800-1000kb of data. This is usually the data that is used on the first sync. The syncs afterwards are just small checks to see if there has been added any new contacts or not and transferring only new or updated contacts. In this scenario we are talking about very few bytes of data.