Can native iOS apps be built with Framer alone? If not, I'd love to get involved as a designer for a project that does
No, Framer is a prototyping tool and the prototype is HTML + JS based.
It is however great for prototyping apps so it could definitely be useful to have a designer make things in Framer for developers coding a native app.
If the question is CAN you, then yes, you could take your framer output files and wrap them in a Cordova project and you would have a functioning iOS or Android app.
But the general consensus is that you shouldn't, framer is not intended to be used in production, performance would not be optimized among other things.