I suppose that's the original question.
I'm going to presuppose that when you say
if one was to commence a missed approach from an ILS in WLG
you mean "if one was to
go-around from..." (which might then become a MAPP or a circuit)
The answer is somewhat dependent on the situation.
1) You are still IMC; say, unstable on the approach (or config warning or other problem) and can not safely continue to VMC, then, even without your saying you have an emergency, ATC would treat it as such- at least in regard to other traffic - and pull something out of the bag of tricks to make sure you didn't collide with anything ahead while you are on the missed approach. It's unusual, it happens sometimes, we drop everything else and make it work. (It will work, because in this situation you are likely to be at least a 5nm final when you overshoot.We have time and space.)
2) You've heard the ATIS, and decided in advance you don't want any part of the circuit, and advised approach control accordingly, we expect the MAPP and have planned for it with the appropriate gap for the last departure ahead of you.
3) You are VMC, have to overshoot on short (ish) final for a more mundane reason (cabin not secure, too high/fast etc) we expect you to make the call and then respond to ATC instructions, which would often/usually be to join the circuit. This could vary depending on the traffic. And
that's the bit, I think, where the problem lies.
What if you have a comms failure at (3)? (Or tower has a comms failure.I've had two in the past two days.)
I'd expect you to choose a course of action, squawk 7600 (which in theory sounds great, but in a high workload situation like this, I appreciate that it might take you a minute to do that, and either fly the circuit or the full MAPP, and be ready to respond to any TCAS warning.
Obviously in a highly fluid environment the traffic situation is changing. At Wellington it's not unusual to get a windshear. (Someone has to be the first on any one day to experience it.) Some companies have SOP's that say that you don't do a circuit in certain conditions of windshear/turbulence.
(3) would be a very weird occurrence. ATC would definitely treat it as an emergency, in regard to traffic management, and get circuit traffic (or IFR traffic ahead) out of the way ASAP. And hope you had a cell phone on board.
Sorry if that doesn't help much.
I'd suggest default #1, if you haven't previously advised approach that the circuit is a no-go, is that you plan on joining the circuit. For us to get a Cessna downwind in VMC out of your way will happen very quickly, once we've realized the necessity. For the radar controller to get a preceding C208 in IMC heading for TY (worst case scenario) out of the way will take longer.Maybe quite a bit longer. There would fairly likely be a loss of separation.