It will let some extra dirt and grit onto the engine. Depending on the environment, it might have mild or severe consequences. Most dirt will probably just blow thru, but some will remain in the engine, and some that blows thru can cause increased wear on valves and seats.
However, I have seen some circumstances where the engine lasted quite a while with an open bellmouth. It really is situation dependent, but it will always increase wear to some degree.
Jetting might be affected, so you should always check it after making any changes like that.