The title kind of says it all: Can the Context User on an Email Service be an API-Only User?
I found this note in the online documentation:
Set Context User – this specifies the context under which the Apex class will run. It defaults to you, but you’re free to pick another user from your organization.
but it doesn't indicate whether it can be API-Only.
UPDATE: When I say "API Only", I'm not referring to a different license type or a different set up CRUD permissions; I'm referring to whether the user has the following User Permission enabled (see http://na7.salesforce.com/help/doc/en/admin_userperms.htm):
API Only User - Access Salesforce only through a Salesforce API.