My suggestion is NO. Do you watch your child taking a math test? Chess games are more like a math test than a soccer game. You can't do cheering or anything. Your child has to fight the battle on the board by himself. No need to stress yourself out and put more pressure on your child. Please read the following article: "Parents' Gambit".
I rarely watch my daughter's games. If I stay in the room, I watch other games faraway from my daughter's board. Nowadays, I don't even bother to check who is her opponent. As a parent, my job is driving her there, providing her food (if in Phily, I don't need worry about that either), and picking her up. She can handle most things that are happening in tournaments at age 8. Even if I were not there, there are tournament directors and other kind adults can help. Always remind your child to get help from the tournament directors, kind of like getting help from teachers at school or getting help from polices on street.
When she won the Susan Polgar National Invitational, the last game was video broadcasted on the Internet with no prior notice. It was tremendous pressure. There was a large screen in the hallway showing the game. Some parents and GMs were watching and discussing. I sat faraway by myself, didn't want to see anything, hear anything or talk to anyone. It's too much pressure, more than if I were playing the game myself. If you don't understand this, please read the classic: "Searching for Bobby Fischer".
In conclusion, relax yourself while your child is playing.