I wan't raised bilingual, but I started studying Japanese when I was 18, and have lived here for over 4 years, and work at a large Japanese company. Most of my life is conducted in Japanese nowadays.
Yeah, my brain definitely thinks in Japanese. Of course it's MY Japanese, which is to say its probably not perfect. Even my nonvoluntary expressions have turned Japanese. Except "Oops," for some reason that is still English.
Of course, if I am in English mode, ie not speaking, reading, or listening to Japanese, like in my free time, it's still primarily English. Like when I'm shopping, my surroundings are all Japanese, so I think in Japanese. When I am browsing the internet, I will think in English.
I guess it's all context dependent, but the tl;dr is "yes"