I’m American (US) but when I lived in Germany, by the end of two years there I thought in German. I remember it, but there are two anecdotes that underscore it:

1. When I returned to the States, I’d occasionally not be able to remember the English word for some things. I lost “trashcan” for a good half hour, once.
2. I occasionally talk in my sleep, and for a few years after I returned my wife would sometimes tell me that I was speaking German.

I didn’t spend much time around English speakers when I lived there; I met my wife the year after I returned, and the person I was seeing when I lived in Germany had barely spoken English.