Would an oxygen supplement help a 3 y.O. With sleep apnea?

Usually not. Most likely your 3 y/o has obstructive sleep apnea, which is caused by upper airway obstruction while sleeping. Usually this is from large tonsils and adenoids and can be treated with tonsillectomy and adenoidectomy. Oxygen will not help the airway is blocked. Some children may have other types of sleep apnea or lung conditions that may require oxygen, so you should contact your doctor.
Only a little. Oxygen supplementation would help keep oxygen levels up in a child with sleep apnea, but would not help with obstruction, good quality sleep deprivation, restless sleep, etc.