ESH. He should not be pressuring you to have children in a way you do not want but going behind his back is a shady move. But speaking as a childfree woman and from personal experience, do not marry this man. You might love each other, but if you have different philosophies on having children this will end in heartbreak and resentment for both of you. Hell, he's already starting to show resentment towards you. There is NOTHING you can do short of giving in and having his biological child that will get rid of this resentment. And if you do that, you will end up getting bitter and resenting him, and then there will be three miserable people instead of just two.

And, not to be to cynical, but there is just no way to know if he would actually approve the procedure if you can't get it before marriage. There are so many horror stories across Reddit and the internet of people getting married and finding out their spouse isn't who they thought they were. You said he's been ramping up his kid talk the past couple of weeks, that's a clear sign he is NOT OKAY with what you have talked about and I'm very concerned for you. If I were you I would keep a very close eye on my birth control, cancel the wedding, and get the sterilization done.