on *:START:{
commands to be performed on startup go in here
}

You can add an ON START event that performs commands only during startup. But for doing this inside a script instead of in the editbox as I described, you'll need to use the 2nd version of the script.

Be aware that the alias works by assuming that if today is Friday, and the alias is given parameters to perform the action on "Fri" at any time of day, it's assuming that you mean the Friday 7 days from now. So if you restart mirc at 2am Friday on the day where the notice should be happening, and if the command is to display Fri 18:00 it will first activate 7 days later.