Yes, but I believe Bürger has connotations in German that citizen doesn't have in English. Ein Bürger is going to be a solid, middle-class guy -- well-off, even, but never an aristocrat -- that's a different class entirely. It goes back to the days when people were citizens of their particular town, and had voting rights there, and had other rights in consequence of their town citizenship.
But in the US, anyway, if you refer to an individual person as "the citizen" you sound, gasp, like a communist (very scary to US folk) even though you can talk about "being a good citizen" and sound perfectly patriotic.
"The townsman" might get a little closer.to what Bürger means in German.
I believe "bourgeois" before the French revolution meant the same thing as Bürger; they were the middle class who had property and voting rights within their towns, and were making money, as opposed to the Aristos who had even more power and wealth, and the starving populace.
So this all gets tied up in franchise, and economics, and class conflict...
No, you can use Bürger; although the etymology of the term is similar to bourgeois, it never picked up those connotations, what with Germany having a very different economic and political history than France.
It just makes it hard to translate into English. If you can, maybe just leave it as "Bürger".
In American English, "bourgeois" is only used to mean "citizen" in the broadest, figurative sense. It is much more likely to be thought of as a specific class distinction of the citizenry. The average American wouldn't consider it to be a synonym for Bürger. Therefore, I would flag this question for removal on the basis that it is a poor choice for learning.