Hmm... I have to admit, after reading a fantasy novel like Tuck Everlasting, I would have to say no. While I don't know if you would still age while being immortal, or if you'd stay the same age forever like in Tuck Everlasting, I wouldn't want things to change around me. Not only that, but because things are changing, people grow up. And that would mean I'd run into adults I knew when they were children. There would be a chance they'd recognize me. And that would creep them out. So, like in Tuck Everlasting, I'd probably have to resort to hiding in someplace that seldom travel by.
I also believe in coming back to Earth anew, as deja vu does happen for a reason. And people have had visions of their past lives, so... I'm not saying I believe in reincarnation (which is completely different than coming back to Earth in a different form without consciously remembering anything in your past lives), but... Yeah.