Taking advantage of the subject in the thread, does that mean that if someone could manage to generate the private keys of that address, could they spend those Bitcoins?
There is no guarantee that address even has a valid private key. However, if it does, and if someone generated it, then yes they could spend those bitcoins.
Or does a Bitcoin burn address have any special technology to prevent this kind of problem?
No.
I know it's near impossible to even generate this custom address but it won't be impossible right?
That depends on what you mean by "impossible".
There are many things that are mathematically "possible", but they will never happen in the real world.
For example, it is mathematically possible that you could make a random guess at the exact order of all the cards in a well-shuffled standard 52-card deck AND get it exactly right 10 times in a row.
But in the real world, that simply isn't going to happen, so we humans call that "impossible".
What would happen to Counterparty if this happened?
Difficult to predict. That would depend on how the users react.
Could anyone withdraw the funds and re-send them to generate other tokens infinitely?
That would depend on what safeguards Counterparty builds into their system.
