No. Brushfire does allow for payments to be made if you've set up your event to allow them, but it does not manage automatic periodic payments until the balance is paid in full. All payments must be made manually by the internet customer or by an administrative user.
We understand automatic payment is a feature that many customers would like, but the complexities involved in processing automatic payments currently prevent us from providing this service. However, we are always working to extend and enhance the functionality in the system and it is possible this feature may be available in the future.