You know, I forgot I had a 2nd character. I did a lot of stuff as mayor before I talked to Katrina so I was like "argh I don't wanna soft reset" but I'll do that as my turnip character and post the results (if anyone's interested).
Long answer: In previous Animal Crossing games, Katrina was the one that determined the type of fortune you'd receive. Not in Animal Crossing: New Leaf. The game is programmed to determine the type of "luck" you'll get for the day just as soon as you start loading up the game (which is essentially saving as well, since it's also saving the daily changes to the town as well as placing a "flag" code in the save file in-case you quit the game without saving). Which means that Katrina will only tell you the type of daily luck the town already has in her fortune.
Short answer: Nope, "luck" changes daily and Katrina will only tell you what type of "luck" you already have for the day. Also, the game saves the daily changes while loading the save data.