If there is a need for it, probably, but we'd need to be able to keep people alive for that long first. To date, the longest anyone has been in space has been 14 months. To make it work you'd need to produce food, artificial gravity, etc.
In Hyperion, people change themselves to fit the surroundings instead of the surroundings to fit them. This makes them Other, and they are the Boogeyman to standard humans.
This may be how it works out in the end. The “Belters” adapt and never set foot on anything with more gravity than a moon ever again.
Only a madman would get onto a generation ship on a one-way non-abandonable non-rescuable trip without seeing the proof of a sustainable colony orbiting the earth first.
Given the acceleration and (eco)system bring-up challenges, I suspect it would take more than one generation from "keel laying" to the ship first leaving the solar system. You'd have a generation living in a partly-constructed colony ship while building the rest of it.
