I may have misread this but apparently every time you generate an address it is not checked against any other addresses generated? The reason being the sheer scale of the amount of possible addresses that could be generated makes the probability of generating two of the same addresses almost impossible. If that is the case, that would mean the same for the private key. What would happen if by some chance two addresses were generated equal?
It is correct: new addresses are not checked against any existing address. Cryptographically speaking, those addresses look like completely random strings (that is they are indistinguishable from a real random string). Interestingly, Bitcoin addresses used in transactions are not even bound to be real: you can put whatever random string (of course in that case you would lose your money :).
Now, still cryptographically speaking, that "almost impossible" means that the probability of that event to happen is the same for you to be hit by a lightning 5 times in a row on a sunny day...(or something like that :) What I mean is that even though the event is mathematically possible, it is impossible in practice.
That said, in case it actually happens, the person who generated the colliding address would also have the same private key, giving them the ability of spending all the coins associated to the original address.