Does TransactionScope guarantee data integrity for sudden shotdowns?

Can someone tell me the principle of how TransactionScope guarantees data integrity across multiple databases? I imagine it first sends the commands to the databases and then waits for the databases to respond before sending them a message to apply the command sent earlier. However when execution is stopped abruptly when sending those apply messages we could still end up with a database that has applied the command and one that has not. Can anyone shed some light on this?

I guess what Im asking is can I rely on TransactionScope to guarantee data integrity when writing to multiple databases in case of a power outage or a sudden shutdown.

Thanks a lot, Bas