Yes, Olga was eligible for a non-immigrant work visa to the USA before she got knocked up. One of the questions that the USA asks on visa applications is for you to list all family members in the USA. If you have family members in the USA, you are at higher risk to overstay. If you're a young Russian woman who gets knocked up by an American, and he takes your baby to the USA, your chances of then getting a non-immigrant/work/student/tourist visa to the USA go way, way down. Also, if she applied for another work/tourist/student visa they would see in the system that she already had a pending K-1 visa to immigrate. They're not going to give her any more non-immigrant visas, because they know she really, really wants to immigrate to the USA. She's eligible to immigrate permanently on a fiancee visa, but she's basically no longer eligible to just visit, because it's obvious she would never want to go back
I agree that the chances of Steven getting the baby out of Russia without her permission are zero. The Russians wouldn't demand to see the baby's American visa, but they would demand to see permission from the mother.
I don't fault TLC for using this storyline. Even if Steven's chances of pulling off his baby escape plan are zero, the fact that he is trying to do it, or threatening to do it, and telling Olga she has no say in the matter, is very revealing as to his true nature.
Now, if Steven has no intention to taking the baby from her and going to America, and they are just making him say that stuff to look like an asshat (like the scripted "Thai massage" line from last season) then yes, that's disgusting, and Steven is stupid for playing along.