UPDATE: API access is not normally supported in GE and PE orgs. However, after your app passes the security review, you’re eligible to use some APIs for building composite applications.
API Access to GE and PE:
Web Services (SOAP) ---> Yes, with token
Apex methods exposed as Web services (SOAP) ----> No
Web services (REST) ---> Yes, with connected app consumer whitelisting
Apex methods exposed as Web services (REST) ---> Yes, with connected app consumer whitelisting
Chatter REST API ---> Yes
Metadata API ---> Yes, with token
Bulk API ---> No
Data Loader tool (uses SOAP Web services) ---> No, can’t set the token