No, it is not healthy and will go nowhere or could turn into an obsession in the worst case scenario. It is better to move on and find someone who is interested

As a pure act, I can’t see that it causes any harm.

However, it will very likely lead to frustration, anger, and poor treatment of the person in question. Those things are bad.

“Should you” as in “is it morally/ethically wrong?” No, it’s not. “Should you” as in “is it a good idea?” No, it’s a terrible idea. And I think you know that on some level.

Don’t do that to yourself. You need to move on.