Does Customer Self Service User has access to custom objects

Summary:

Does the self service user has a restriction in calling the custom object from the script written in SR object

Content (required):

Need to automatically create activity under an SR , when an SR is created from an end user in DCS portal . The Subject and the owner of activities are picked up from a custom object using groovy . It is not working as expected . Does the self service user has a restriction in calling the custom object from the script written in SR object since the user doesn't have the custom object administration role

Version (include the version you are using, if applicable):