Yes, to do this, you will want to use the Add Student to Homeroom endpoint at https://[your_sub_domain].classroomparent.com/e/cr.
This endpoint will work even if the students are already listed in the homeroom, as it allows a parent to select from the list of students in the homeroom, or add their own.
To use it, you need to provide parents with their students homeroom class_code (which hopefully they will already know, as it should align with the class code used at your school), and the homeroom password.
You can get both of these from the Classrooms Export in the Admin/Exports area. In this export, you will see a column for the class_code and for the password.
When a parent navigates to the Add Student to Homeroom endpoint, they will be asked to enter their homeroom (classroom) class_code for the student they want to add, and the associated password. Once they enter that successfully, they will be asked to select a student from that homeroom, or will be allowed to add a student to the homeroom.
IMPORTANT: Do not publicly post the passwords. These should only go to your school community, preferably, only the parents in a homeroom will be given that homeroom’s password. At any time, you can reset the classroom password by editing that homeroom and selecting to have the password reset.