What will happen if hook hose coming from Crank case to carb overflow

ok, I have a few questions;

First, is this a four stroke or two stroke engine? I will assume you have a four stroke GY6 based moped or scooter. The GY6 design is one of the most common.

Second, I’m not sure you are naming things correctly. The hose the comes from the crank case (should actually be the valve cover) should go to the airbox (air filter housing). The other thing that can be done with that hose, if you do not have an air cleaner is to use a breather of some sort. You can just run a long hose, placed higher then the engine and open to the atmosphere. Just keep in mind, not just crank case gases come out of the hose. When run hard, you can get oil in that hose as well.

What are you calling a carb overflow. Is it the hose coming from the bottom of the float bowl of the carb? If so, that’s a float bowl drain. You open a valve at the bottom of the carb (in most cases) to drain the carb so you can store it, empty.