Yes, TOS has a great conditional order capability. They are definitely not held on your machine, that much I know.
Sorry, I edited my post once I saw your other question. So again they are not held on your PC so you can easily log out, turn it off and the orders would still be working.
TOS is becoming a more powerful broker that most people think. I dont know where most of the orders are stored with futures but i know of forex that they store the orders on their severs so that the crooked ECN's wont stop hunt your stops. They continually update their platform. Its more powerful than what you think.