Since he is really from India and came to the US when he was 18, I would presume that his "real deal" is the Indian accent. Being a talented actor, he can probably accurately simulate a variety of American accents. He spent several years in Portland, Oregon, which has very similar intonations as much of California.
Since he was only on one episode of Sullivan & Son and I did not see it, however, the discussion of his American accent(s) is mostly speculation on my part.
Here is what he says about his own accent (from IMDB.com):
Originally Posted by Kunal Nayyar
I have a dialect myself; it's more pronounced, because I have studied theatre and been in England. It's half-British, half-Indian.