Not from the meaning of the words however - "expat" describes your relationship to your former country, and "immigrant" describes your relationship to the country you are currently living in. So if you live in another country than you were born in, you're actually always both at the same time - i.e. an American expat living in Germany is an immigrant to Germany.
Are they? I have a couple of Russian expat friends on Switzerland and Germany. This might be my bubble and I appreciate your calling out a bias in who we think of as "foreign" but I'm not sure it's this clean cut