“Ah, yes, the ‘Who Wants To Live Forever?‘ trope. The unbearable ennui that allegedly awaits all immortals. We have dismissed this claim.”
Basically, no. That’s just what mortals tell themselves to make their inevitable ugly demise look prettier, in a grand form of Stockholm Syndrome. The universe is a big and fascinating place, and there isn’t any particular ceiling on personal growth, and if it turns out to be a problem after the first terayear or so, well, we’ll make another one where we can be something different. With blackjack! And hookers!
(Also, all your friends are also probably immortal, and when you meet one who isn’t – well, you can fix that, which is a much saner response than sitting around wangsting about it. So, yeah, basically Living Forever Is Awesome. In your face, Grim Reaper!)