You'll need cryo pods as well, because you can't actually store population on a ship, you store "cargo" of people. I think a cryo pod is 10k people? So you'll need 1:5 for OH and Cryo. Doing this, you should be able to load your ship with colonists, then abandon colony.
There's... several problems with this, but three are most notable. 1: Upkeep cost will be outrageous, so you'd have to turn off maintenance. 2: It will probably be too slow to catch up to many planets, so you may have to go after asteroids with orbit turned off, or fly the opposite orbit from the planet and try a "head on" approach instead of "chase" approach. 3: If you do make it fast enough to do anything, your fuel consumption will be astronomical.
Do also keep cargo in mind. 5 pods are needed to move most structures. 25 pods are needed to move large structures like research labs and terraforming facilities. You'll also need to carry your wealth on your back, so mineral cargo will be a concern as well. 50k population doesn't support much either, I don't think it will man even one lab, and I think a single mine uses 10k. In the end, you're looking at a ship the size of a planet when you account for living space, cryo pods, cargo pods, and massive massive massive fuel tanks. Population considered, you'll probably want to mount asteroid miners and sorium harvesters as well, because I believe they're actually more size-efficient than the cargo pods and population required for a mine/fuelery.
This ship would take, probably, on the order of centuries to produce. Thankfully the OH makes it possible to construct it with Industry instead of Shipyard.