Nathaniel Branden, who has done much of the work on self esteem, defines it as below:
"Self-esteem is the experience of being competent to cope with the basic challenges of life and of being worthy of happiness. It consists of two components: 1) self-efficacy—confidence in our ability to think, learn, choose, and make appropriate decisions; and 2) self-respect—confidence in our right to be happy; and in the belief that achievement, success, friendship, respect, love and fulfillment are appropriate to us".
As you can see, part of his definition is the right to be happy. So, at the very least the two, (self esteem and happiness) overlap and are related.
However, theory is one thing and practice is another. Probably better to work on self esteem (it's a learnable skill), and notice what else happens!