If you stay eternal young, then yes.
Everything boils down to that everyone will die and you'll stay alive.
Granted there is no difference to how it is now, being mortal.
I know I will outlive my parents (unless i die of accident or anything else), just as they outlived their parents.
Friends will die, sure, but you can always get new ones. I lost contact with alot of people since...kindergarden and gotten new ones over time as I grew up.
Companionships, well alot of people re-marry these days and time heals everything even if you dislike remarrige.
What I mean to say is; Every person goes through this and can handle it. Only difference is as a Immortal, you'll experience it alot more. Myself I don't see it as a problem. If you're born with it or make the decision yourself, is another matter.
I'd rather make the decision myself (choose to be immortal that is), then having it put onto me by birth. Why? Because I believe myself to be mentally capable of handling it.
Now people say it can be boring after some millenia,
What would be boring? You can basically do everything and due to the human society, things will evolve and there will always be new things to do.
We don't know what will happen in 100 years, but if space exploration and colonization will become reality, even better. New planets, new things.
What would really suck is if humankind dies out and you're left alone, but even that doesn't mean it the end. You have a infinite time to travel searching for aliens or hell make new humans if you have the knowledge, and why wouldn't you? Read books dammit. Yes you'd be God in that sense.
The best part though: No need to take out the trash. It will turn into dirt if you wait long enough.
Ps.
Take it with a grain of salt.