I don’t believe there is any evidence that vitamin C reduces inflammation or helps with depression. Vitamin C is an antioxidant, not an anti-inflammatory agent.
There is evidence that things that reduce systemic inflammation help with depression. Fish oil, or more generally a balanced omega-3/omega-6 intake is one example. Curcumin is another. However the effects are modest, which is probably to be expected with a condition as diverse as depression.
„Vitamin C supplementation attenuates the oxidative stress (lipid peroxidation) and inflammatory response (IL-6) to a single bout of exercise.“[1]
Vitamin C is essential and gets consumed by the body and needs to be replenished. For example during sickness the Vitamin C consumption is higher which could lead quickly to low levels.