You can delete a contact from your database at any time. In deal they have an existing deal (regardless of the status) they will appear within it as "Name Last name (deleted)" so that you know you deleted them from your database.
When you delete a contact you only remove their information from your contact database, their existing deals, or your conversations with them will remain untouched.
Deleting contacts in Funnel doesn't touch the data in your Gmail or Google Apps account, including email conversations, address book details. They will not be modified or removed by Funnel in any way.