I would say that Pink's has equal parts local following and tourists (and celebrities, although the celebs don't always go there in person, but I will explain that in a second). I am 43, but I remember long lines for Pink's way back when I was 14 and chowing down on their chili burgers! It has grown in popularity over the last few decades, for sure, but it has a diehard local following.
As for famous people at Pink's, a lot of the entertainment companies in this general area - and there are many - send their runners/assistants out to get mass quantities of Pink's Hot Dogs to bring back to the offices, or they order a bunch of Pink's stuff for cast parties and things like that. Every now and then a few celebs show up at Pink's - there is a famous story about Bill Cosby showing up there, for example - but mostly they order things to be sent to them on movie sets far away or they have their assistants do the dirty work and get the food for them.
Another reason why Pink's spiked in popularity - other than word of mouth - over the last decade is because another local favorite hot dog place - Tail o' the Pup - closed down. TOTP had a different kind of chili - it tasted different than Pink's, but was very yummy and had a definite following. TOTP was the place that is famous in photos - you've all seen it. It's the giant hot dog with a window in front. It was an iconic part of L.A. scenery, just like the giant doughnut that belongs to Randy's Donuts.
So when TOTP closed down, sadly, I think a lot of the chili dog lovers migrated over to Pink's, and crowds increased. I guess there just was not enough room in this town for two hot dog giants!!