If i have sleep apnea and depression, will the apnea improve if i improve my depression?

Unlikely: It's the other way around... Improving the apnea may improve the depression.

Usually opposite: Usually improving apnea improves depression not the other way.

See below: It's more likely the other way around. Your depression is more likely to improve if your quality and amount of sleep improves. You may need a sleep study for a complete diagnosis.