So two things happen:
They convert. Run to the nearest US embassy and claim asylum due to religious persecution and Welcome to the USA. And the taxpayer pays for it.
Your convert is exposed and they get their heads chopped off.
Awesome!!!
What you are suggesting isn't what happens.
Christianity is the fastest growing religion BY FAR in some areas of the world (mostly among Muslims). They don't run to the U.S. embassy because there are no embassies near them.
They blend back into their cultures and spread the Gospel.
Study up a little on this matter. I think you'll be shocked (positively) to find out what is actually going on.