If you did get married, what would your reasons be?
I assume "getting my spouse citizenship" would be a benefit rather than a primary reason.
List the reasons that you would have to get married. Then, tell her if she brings the topic up again, you'll be walking away. If she sidesteps, continue to talk about it no matter what. Marriage is a big deal, fraud aside. Let her know that you won't tolerate her joking/not really joking pressure. As much as you sympathize with her problem (and please let her know that you do) you are not the answer to it. Period.
After this conversation if she talks about other things, engage. If she talks about this walk away, after you warn her.
My strategy in these situations is an attitude of cheerful firmness. If you get mad or annoyed, other people do as well. I set the rules of engagement, stick to them, while remaining as cheerful as possible.
You can't actually make other people be or feel a certain way. A heartfelt talk where you really talk to her about her situation and that you are not going to be the solution to it, where you empathize, NOT avoid, and talk it out, ending with you stating that her joking about and bringing it up when her need is so raw and real and you CAN NOT be the solution, makes you uncomfortable. And now, here are the rules if she does bring it up.
Either, a) you will not answer her or respond in anyway or b) you'll be walking away from the conversation for a minute.
Then, do that. If she gets mad or asks about it, you cheerfully say, "we've talked it out, I'm doing what I said I would. You're choosing to bring it up, I'm just keeping up my end."
And have a new topic of conversation ready IMMEDIATELY.
Rinse and repeat.
It sounds as though she's spotted you out as a person who caves to social pressure. And she's doing what she thinks might get her the desired result.
As to whether you will still be friends, that's up to her. It's not up to you. All you can do socially is set the terms of engagement (oooh no pun intended) and stick with them. People will get angry when they don't get what they want, but you cannot control that, unless, of course, you always give people what they want for fear of them getting angry or rejecting you. This may be the way you generally deal with the world, but make it clear that it will not be the case in this instance. Please don't get married just to be polite.