Does low oxygen saturation cause brain damage ?

Possibly: Possibly, if low enough for long enough.

Low O2 & Brain Inj.: All the cells in our body require oxygen. Our bodies have a lot of infracstructure to secure this: lungs, heart, blood vessles.... It is why airway, breathing and circulation are the abc's of resuccitation. If the oxygen saturation is low enough for long enough the effects are irrevesible. The brain is particularly vulnerable. It takes a few hours to lose a limb, a few minutes for brain damage.