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.
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.
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.
This sounds like it ends with a xenomorph bursting out of your chest.