Well, not exactly....
You have to remember that, for a missed approach, there is a certain required climb gradient. If there is no minimum climb gradient specified in the missed approach procedure, then the standard certification figure applies. (Can't remember off hand....I'm thinking it's 2.5%. Please refer to the Airbus doc "Getting to Grips with Aircraft Performance.") If the requirement is greater, the approach plate will specify.
In the case of the standard required gradient, your aircraft should be able to make it with one engine inoperative. In the case of a higher-than-standard required gradient, well.....maybe yes, maybe no.
You'll have to get into the performance charts to make this determination. If the result of your research is positive, all is well. If not, there are two ways to go about this.
First, you can increase your DA, thereby giving your aircraft a 'head start' for the climb. For example, on an ILS with the typical 200 foot DA, you might increase your DA to 1000 feet.
Of course, you, as the pilot, cannot arbitrarily make this determination. This is part of the IAP certification. An example of this would be Hong Kong's ILS to runway 07L.
Or, second, you could fly the standard ILS, but, in the event of an engine failure at go-around, fly the 'engine failure on takeoff procedure'. In the case of your aircraft not being albe to maintain the higher-than-standard missed approach climb gradient, this would provide you with protection.
Doing so is perfectly legal, required, and expected......
So, to say that this procedure is for take off only, is incorrect.
In any event, either an engine failure on takeoff or missed approach, notification of ATC is required, so they are aware that you'll be flying the one-engine-inoperative profile and not the standard missed approach procedure.
Should you include all this in your standard approach briefing? What does your company's SOP say? My old company required it. Perhaps your company's SOP does or does not.
If it does not, then such a briefing falls, not into the 'SOP bucket', but, instead into the 'technique bucket'. I never chastised a pilot for anything in the technique bucket. If it's not explicitly stated in the SOP, but the pilot wishes to brief it, anyway....well, this, in my opinion, is good airmanship (airpersonship). Good airmanship is not stressed enough, these days, in both our fundamental training an our routine line operations.
I hope this provides some insight...
Fly safe,
PantLoad