Is being a sex slave a good thing to get over depression?

No. More than likely, the sexuality will make you more depressed, as you realize there should be more to sex than someone else's pleasure.

Also-it is just an avoidance practice. We cannot rely on anyone else to make us happy, and being of service eventually leads to burnout if it is not balanced by your other health needs

perhaps you should get into treatment and figure out what is causing your depression.