Yes. You need to give anonymous user Access IForm privileges as you have done. Then on the submit form, edit the form and find the "Other IForm Parameters" section. Tick the box "View access control" which lets you take fine control over who can access this specific form, then fill in the box "Permission name for view access control" with the name of a permission to create in Drupal (I normally use "online recording" as the value for this box, unless the page is specifically for administrators or coordinators of some type).

Now, you need to give "Online recording" rights on the Drupal permissions page to the Authenticated Users role. Then only authenticated users will be able to see the form.

Best wishes
John