There's a setting for iOS that hides the contents of SMS messages on the lock screen. With that, they'd at least need your pin. Hopefully you'd have some printed out backup codes.
SIM PIN codes seem to have gone out of fashion. Neither my UK SIM nor my US SIM, both bought within the last two years, had a PIN code out of the box. Of course it's possible to set one but that's buried somewhere deep in the phone's settings, so most people probably don't set one.
I didn't even know it's possible to have no PIN code on a SIM card!
Operators in Finland always give you PIN cards with a preset code like 0000 or 1234, and tell you to switch it in their quick start instructions. I'm sure many people leave it as it is, though. Almost no-one seems to know you can actually set it to be more than 4 digits.
This looks like an area that phone operating systems could fix – by making it easy to change your PIN, and encourage using more than 4 digits for it.