Let's say the Large Bitcoin Collider manages to guess the private key of a particular Nano Ledger S. Can they then 'spend' or 'steal' the Bitcoins on the Nano or 'send' them to another wallet?
If LBC is somehow able to guess anyone's private key, regardless of how the private key is normally stored and generated, then yes, they can just spend the coins. All you need is the private key, it does not matter how the key was obtained.
Of course this is impossible to do in practice with today's technology. The range of possible private keys is incredibly large, much larger than a human can imagine. If the private keys were generated with sufficient randomness (which Ledger Nano S's do as they have a True Random Number Generator), then the probability of generating a private key that is in use is so small that it is effectively zero.