If they're self-sufficient, they could survive. Human population on Earth has bottlenecked to less than 100,000 in the past and we recovered.
That is, they can bring a lot of fancy stuff with them, but to be self-sufficient they'd have to be able to maintain, repair and ideally rebuild what they need indefinitely without resupplies from Earth.
I think that it could be possible for them to focus on few important/key paths, in theory. But, unless they research and prepare for exactly that scenario and chances that it works would be strictly in their favor and they all would work hard, learn hard and motivate themselves through their entire life, I don’t see how it could work. Not to mention political, social, religious risks with the next generation.
I’m not 100% sure ofc, that would be no doubt an interesting “experiment”.