Can I remove the Add button to prevent adding account addresses?

Unfortunately, the Addresses region in the Edit Accounts page in classic Sales isn't extensible. However, you have a couple of other options to prevent users from adding account addresses.

Option 1: Remove the Manage Address Privilege from Role

Even though you can't remove the Add button using Oracle's configuration tools, you can remove the privilege, Manage Address, from users' roles. Users without the Manage Address privilege have read-only access to addresses. See How do I edit job or abstract roles? for more information.

Option 2: Use Single Address Region in the Edit Accounts Page

There's another option as well. You can disable the multiple addresses region and enable the single address region instead. This will remove the Add button, because then only one address can be displayed in the Edit Accounts region. See How can I enable multiple addresses for accounts? for more information.