Yes, it is. You can even use the Salesforce REST, SOAP, and Metadata APIs (even though Group/Professional edition orgs normally don't support API access).
It's buried in the ISVForce documentation, but the information does exist on two pages:
From the first page (emphasis mine):
Your app can contain business logic such as classes, triggers, email services, etc. written in Apex. As a general rule, Apex is not supported in GE/PE, so it will not run in these editions. However, Apex developed as part of an ISV app and included in a managed package can run in GE/PE, even though those editions do not support Apex by default.
You must be an eligible partner with salesforce.com and your app has to pass the security review. The appropriate permissions will automatically be enabled after you pass the security review.
Here are some important considerations for using Apex in GE/PE.
- GE/PE customers can’t create or modify Apex in your app; they can only run the existing Apex.
Your Apex code should not depend on features and functionality that exist only in DE, EE, UE, or PXE, or your app will fail to install.
- Make sure to use REST if you plan to expose an Apex method as a Web service. Apex classes that have been exposed as a SOAP Web service can’t be invoked from an external web app in GE/PE.
- Using Apex to make Web service callouts is allowed in GE/PE. For instance, if you’re planning to make a Web service callout to an external Web service, as long as the managed package is authorized, these classes will function in GE/PE.
From the second page:
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.
- Currently, the standard Data SOAP and REST APIs are supported for GE and PE apps, and Metadata API is supported in PE apps. To request API access, see How do I get an API token for my app? You can also contact Salesforce to request that a connected app be whitelisted to use the REST API in GE or PE orgs.
- Other APIs, such as the Bulk API and Apex methods exposed as SOAP Web services, remain unavailable.
- You can enable REST-based Web services using connected app consumer whitelisting.
- You can enable SOAP-based Web services, including Metadata API, using an API token called a Client ID, which is appended to your SOAP headers in integration calls. This special key enables your app to make calls to GE and PE orgs for Data API and PE orgs for Metadata API, even if the customer does not have API access.