I saw a thread for this, but after much searching, I can't find it. Its a thread about getting a quest to start when you load your game, so that you can have a "X's Mod loaded!" message come up, along with all the other junk you put in it.

If you do not set any event for the quest, you can tick "starts the game enabled". That should start the quest on game startup. Or just use an OnInit() Event for the messages.

Will this load up the quest if I load up a savegame that previously did not have the mod, or will it require starting a new character?

It will start the instant you start playing a game where it is not already started, new save, old save, it doesn't care.

A previously unseen 'start game enabled' quest will start at the next savegame load.