The short answer is no, you don't need Alfresco in your delivery environment in order for launch and expiration dates to function.
The long answer is that effectivity periods and deployment in Alfresco are handled at different stages in the content lifecycle, so don't directly interact. In particular timed launch controls when content is promoted to the staging sandbox, and does not (as is often assumed) control when the content is deployed.
The expiration date is even more misleading, in that it's simply an advisory date - the Alfresco system actually doesn't do anything beyond creating a task for the author when the expiry date is reached. The user then has to choose what they wish to do with that content (eg. delete it and submit the deletion to workflow).
