@JESSICAMUNN It definitely should be possible for students to make two different types of submission to the same assignment, though they will need to make two separate submissions to the assignment to be able to submit both an annotation and a Google Doc.
You can do this by creating an assignment with an Online Submission type and then selecting both a Student Annotation and File Upload as the submission types. Make sure you also allow at least two attempts on the assignment as well. Then students can make and submit the annotations in one assignment attempt and add the Google Doc in another attempt. You will be able to view and grade both submissions from SpeedGrader but selecting which attempt you want to view from the dropdown at the top-right of SpeedGrader.