You can see the threads they make, you will see that they made a post and you'll see a message that it's being blocked, and a link that allows you to click it and see what they posted.
They can see everything you post unless it's been deleted, or unless they're mods/admins (you can't put mods/admins on ignore), or they've put *you* on ignore and then they see what I've described above.
At least, I'm pretty sure that's how it would work on this board. You can test it on me if you like. I could even proffer a... fuck you, if it would help. I wouldn't mean it, of course, just use it like a prop.