Yes, both parents and students can sign a school form. You'll need to add the blocks User Signature and Parent Signature when editing the form.
Article
Number:103535
Products:
Blackbaud_School_Management_Platform
Once you add the blocks and have the form published, only the user logged in will be able to sign for themselves. For example, if the student is logged in and filling out the form, they will only be able to sign for themselves and vice versa with parents.