NO! Take responsibility for not doing what you were suppose to! Don't "play" like an immature student.
I want to say sorry to my teacher for not turning my homework in on time. My baby cousin says he’ll cheer them up by writing his name and write them a drawings. Should I let him?
No
Grow up and take responsibility for your own faults. That teacher doesn't need cheering up, they need you to do your work.