Do you think suicidal patients, especially when treated, could follow through, not only because they're depressed, but also because the happiness at life takes away their fear of death?

….” especially when treated” ?
Would mean that they would see that life has more to offer them and thus No.

Not likely.

People commit suicide because they hate life. If they become happy with life, what’s the point of dying?

And also if a therapist manages to treat someone into committing suicide, I say they fail their job.

Lack of fear of death is not what causes people to try to kill themselves. Life being unbearable is the reason people try to kill themselves.

Happy people don’t try to kill themselves for kicks.

There are some people who do not fear death, and might be more adventurous, or reckless, and may engage in unsafe behaviors for kicks that could kill them, but killing themselves is not the purpose of engaging in the dangerous acts. Having a thill is the purpose.