Well, shoot me for all the times I've struck up conversation with people I run into on a daily basis -- those I know well, don't know at all, recognize, or after talking a bit, realize they know a friend of mine or I a friend of theirs. IMO, dont be an a-hole, but be a civil human being talking to another human being in your approximitity. Katy isn't untouchable, she's very human and more relatable than most, lol. If she sitting down in a restraunt eating (or something more private/personal)... that's different. But if she's... walking down the same side walk, crossing the same street as you... be friendly and open you're mouth to say HI! Spread the love! LOL IMO, of course. 
I wouldn't bombard her or even attempt to go up to her if she say having a meal or something private and personal like that, but if I saw her walking in the street I would love to know that i wouldn't upset or offend her if I was to go up to her and say Hi, ask how she is and see if she would pose for a picture oppurtunity that's all. I know Katy is a WHOLE different league to footballers but my fella saw a footballer he admires when we were away a few years back and walked up to him, asked how he is etc and he posed for a photo - kinda hoping Katy could possibly do the same.
I would never even do anything if it is going to upset her. Knowing my luck anyway she'll probably be away in a different country when I am in LA lol xx
Katy if you're reading this Hi and might see you in first 2 weeks of September ;-)