Yes, they can. If you or your members want to block another member through chat, in the chat window with the member, click the three-dot menu then choose the option to block the member. When you block a member, you will no longer receive notifications or 1-to-1 messages from this member. You also won’t see their posts in your Activity Feed. You can read more about blocking a member here.
Members will receive notifications for chats if they have the setting turned on in their personal settings. They can also mute notifications for a specific chat conversation.