What happens when two txid's collide?
No. After transaction A is included into the chain, transaction B is invalid, and will not be mined. If it does show up in a mined block, the entire block is invalid.

It wasn't always like this. Initially, if a transaction had the same txid as a previous transaction, it would overwrite the first one. Then, if that block was reorganized out of the chain, the second transaction would be removed, but the first transaction would not be added. In other words, adding and removing the block would change the state of the unspent transaction set.

That was clearly ricidulous, so under BIP 30, including a second transaction with the same txid when any output from first is still unspent is invalid. It used to be enforced by the timestamp of the block, but it is now applied to every block in the blockchain except for the two that break this rule.