When someone has an accent, yes, but I could tell you plenty of stories about Angelinos not wanting to address the topic of enthnicity of people based in their looks or their name. I just know from experience, from having worked with a lot of people in L.A. that the typical human resources person at a company would rule that you not ask or mention it.
Meanwhile, in New York City when it comes to diversity they are much more upfront about it. You can tell just be asking what neighborhood someone lives in. I ligved in a Ukrainian/japanese neighborhood in Manhattan, but also with a row of fantastic Indian restaurants one block away. I think it is because it is a landing place for so many immigrants while Los Angeles is more of a place people move to when they want to get away from their past.
In cruising we are VERY upfront about ethnicity or nationality because we have ships where all the crew come from almost anyplace in the world, and so it is a very normal topic of conversation, Crewmembers even list their nationality on their name tags on many cruise lines.
I admit, I don't care for Los Angeles as a society very much. I never found the people there to be as up front and honest about things as I like. A New Yorker will tell you if he isn't interested or offended by something you said, but after he tells you he is done discussing it. No harm done.
In Los Angeles people will prevaricate and not say what they really think, and they will let you waste time discussing something they are not interested in or agree with and act like they agree with you. Hence if you live there you soon get paranoid about what people are really thinking, because they rarely really ever tell you.
Especially when it comes to work. An Angelino will say "oh yeah, we're on it," or "we'll talk" when they really don't mean it. It's like a guy saying "I'll call you" just to be nice.
I should say, really, that I think it is a major cultural different between the east coast and the west coast. I have found people here in Phoenix and up in Seattle to be the same way. I prefer the New York way, myself, but a lot of West Coasters find New Yorkers very brash. They are brash, but in the long run, it works out better societally, I think.
Just a theory, I think to have to live in both places for awhile to understand what I am saying.