You have to take into consideration that this slow starship will take 4100 years to reach Alpha Centauri, if what you say happens and it is bypassed by more advanced ships, the slow ship would still arrive 4100 years in the future around the years 6200 AD, by this time after 4100 years of technological advancement, I would be surprised to find flesh and blood humans populating the system...
Which means our putative cybermen would have passed your space ark fifty times on the way to and from alpha centauri and will be fully aware of its position and nature. Even if you send it off to some other distant star system, you merely give the cybermen -- or worse, the Dalek hordes they later evolve into -- more time to develop a warp drive capable of intercepting the ark and destroying it. The craft therefore utterly fails to escape the human hyper-evolution which, due to the growth of technology, is destined to expand the Cyberman/Dalek/SuperBorg empire much faster than the generation ship can actually fly. And this before we consider the AI you've already placed on board the ship which otherwise COMPLETELY defeats the purpose of building it in the first place.
I've said before, and I'll say it again: bury the embryos in a bunker and tell no one where it's hidden. That would accomplish the exact same goal as the generation ship, except 1) no need for an active AI custodian 2) no risk of damage in interstellar space 3) smaller risk of accidental discovery 4) the bunker has the ability to activate the embryos in the event of a catastrophe and would thus actually succeed
in populating a habitable Earthlike planet. Most importantly, that
project would about 1000 times cheaper; while still far from practical, it is at least feasible
Think of it this way, if you buy a ten year life insurance policy on your self, and within that ten years you don't die, would you feel that was wasted money?
That depends on how much money I spent. $30 a month for ten years aint all that bad in the scheme of things; it's a small expenditure, just in case.
The time and expense of building a generation starship is not a small "just in case" expense. People who are afraid of the nuclear apocalypse build a bomb shelter in their back yard and stock it with emergency supplies, bottled water and shotguns; if nothing happens in five decades, at least it's an interesting place to stash the loot from last month's bank heist.
You know what they probably DON'T do? They don't buy ocean liners and then maroon their children on them with fifty years worth of food and no particular destination.