Yes, if an Event registrant chooses to Pay Later during their transaction a Invoice can be automatically generated for the owed balance. Within the setup of the Event, after turning on the "Allow Purchaser To Pay Later" setting, a new option called, "Automatically Create Invoice if Pay Later" will appear. Turn on that setting, and you will be able to set which Payment Page will be connected to the invoice and how many days from the Transaction Date will the Invoice be due.
This Invoice can then be sent to the registrant using the Mail Merge function on the Invoice grid. To navigate to that grid go to Workspace>Transactions & Invoices>Invoices.