My child scored 20/40 near on a vision screening; does she need glasses?

Glasses or not. If your child is having trouble reading, headaches when reading, or trouble seeing the board at school, then he/she should see a pediatric ophthalmologist to be checked for glasses. If your child is currently driving, glasses are very important!
Maybe. Maybe. That would be a good reason to get a full eye exam for your child. Visual problems when young can lead to permanent vision loss ("amblyopia"), especially if the eyes don't see well at all (not your child) or don't see equally (possibly your child).