Can Alumni keep using the institution email after they graduate?
Only if you licensed them correctly, No CALs but External Connector licenses are necessary:
How to Buy Exchange Server 2007: Pricing and Licensing Information
Note: The External Connector license (EC) is an optional additional server license for external users that enables access to your servers running Exchange Server 2007. With this license, you do not need to buy individual Exchange Server CALs. The EC license is purchased for every copy of Exchange Server 2007 that can be accessed by the external user. An example of an external user is a person who is not an employee or similar personnel of the company or its affiliates. This license allows access to the Exchange server by an unlimited number of external users that can include, but is not limited to, business partners, suppliers, customers, retirees, and alumni. It is licensed per server.