It goes to the airbox? No, that wouldn't cause a problem. There is no vacuum in the air intake tube. Engine vacuum is inside the intake manifold, on the other side of the throttle body. Vacuum is what happens when you suck the air out of a space, and new air can't get into that space to replenish it. This is why engines have lots of vacuum at idle, and not when they're at WOT: At idle or light throttle, the pistons are moving down on the intake stroke, sucking air out of the manifold and into the cylinders, while the throttle body is closed (or mostly closed), thus preventing the air in the intake manifold to be easily replenished, and that is what creates engine vacuum. If the throttle body is wide open, there is no engine vacuum because the air in the intake manifold is easily replenished via the wide open throttle body.
The engine should run exactly the same with that hose disconnected. The only reason it's connected to the intake tube instead of being open to the air is so it sucks in CLEAN air that has already passed through the air filter, instead of sucking any airborne dirt and dust into the crankcase.