No, the OnTimer setting only exists for as long as the window in which it is "set" is open. It will "die" when you quit the runtime.
You can set a field the first time the file is opened that records the date. Your script can then check this script each subsequent time the file is opened to determine if 30 days have elapsed. Users, can of course, play games with their system clocks to keep opening the file, but with many systems, such tricks foul up other date related actions in the database and so this is still a fairly good way to limit your runtime's usability.
You could also use a field to count how many times the file is opened and use that count to limit the demo's life expectancy in a way that does not rely on the system clock's date.
Great answer Phil. I like the count idea. This may be a great temporary solution vs purchasing a plugin or other software to protect my solution.