We are on the same page. What will happen with the emergency is a function of the head height. It may or may not go siphon depending on the head height. What will determine the head height will be the actual flow rate. So far so good?
We know that an open channel cannot handle the flow that a same size siphon can. Why? Because an open channel cannot become a siphon, because there is no way to stop the inflow of air. However, for back up for a siphon, the "backup" must be capable of flowing the same amount or more than the siphon. So far so good?
Now comes the tricky part with open channels. (aka dursos, etc.) The amount of water that can be in the pipe is inversely proportionate to the amount of air in the pipe. E.G. the less air, the more water can be in the pipe, and the more air in the pipe, the less water can be in the pipe. This is where most folks get off the boat. By putting an additional air inlet in the pipe, you reduce the amount of water that can be in the pipe, by increasing the amount of air in the pipe, and exacerbate the issue you are trying to solve.
The DRY emergency will go to siphon, once the head height is sufficient, to not suck in air. We know that is only a couple inches at the most. (basic operation of the system.) What will happen is the water level will rise, till the emergency is handling an equal flow to that of the siphon before the siphon became occluded. It will not be a stable siphon as the water level will drop, (the dry emergency has higher capactiy in most cases, unless you follow the fractured method of a "trickle of flow" in the dry emergency,) and the siphon will break. The process will repeat. If the dry emergency cannot handle the flow period, either due to insufficient head height (implementation error) or "normally having" flow in the dry emergency, or adding an air hole to smooth out the flow, what the emergency pipe cannot handle, will go over the top of the tank, and on the floor.
Despite the hobby standard of "anything works," siphon systems are fairly close tolerance. There are right ways and wrong ways to implement them. If implemented the right way, there is seldom any problem with them, (other than air leaks) if implemented the wrong way, there are problems with them. The nice thing is due to their predictability, they are very easy to troubleshoot. The list is very short, and they are all implementation errors.
The short answer is, you don't need a hole in the top of the dry emergency, and you don't want one.

The ops problem was the emergency was airlocking, because it could not purge the air out. The reason was it was too deep in the sump. Adding more air, would have made the problem worse, not better.