Signalling before braking is a defensive riding skill, to be used when you think there are riders close behind. In my answer to one of the linked questions, I wrote
If you think there are bikes behind you, signal with your hand (palm facing backwards) to show you're slowing and they should too, or call "SLOWING!".
The idea here is that while bikes crashing into you from behind can cause you to crash also, it's more likely to cause them to crash.
As you say, in time critical situations, you may not have time for signalling, in which case I recommend calling "SLOWING!".
You can argue, as many do, that cyclists should not be so close behind you. The conventions I have described originate in group riding situations, where a bunch of riders are in close proximity. They may be social riders, club riders, commuters, or organised ride participants. I have experienced these signal conventions in Australia and Europe.
The biggest danger is when random commuters ride close behind one another, since the rider behind doesn't know anything about the skills or experience level of the rider ahead. So, to answer your question, in the context of commuting
Is this considered safe/advisable?
No riding close behind a commuter in traffic is not considered safe or advisable.
Two cyclists should only ride in close proximity when they both know each other's skills, and are both comfortable to trade the benefits and the risks. In a commuting situation that is not the case.
Edit in response to David Richerby (thanks David for heads up)
Is braking one handed safe?
How safe it is depends on whether you can maintain control braking while steering one handed. It's certainly an advanced skill. When the situation is too urgent then focus on braking and control. If you're worried about following bikes, then call out as I suggested.
If you have time, I do recommend signalling first.
The answer by muphblu led me to investigate what international standards for hand signals exist. I'm not going to reference what I found here, because it's a complete mish-mash.
To summarize, many places still allow riders to follow outdated rules adapted from the rules for motor vehicle drivers (and they were probably adapted from horse cavalry, but I digress). These require
for a near side turn (left turn in Australia, NZ, UK, et al, and right turn in US, Canada, Europe, Russia) to be indicated by holding the other arm out horizontally, with the forearm vertical from the elbow and hand facing forward.
for an offside turn (right turn in Australia, NZ, UK, et al, and left turn in US, Canada, Europe, Russia) to be indicated by holding the same arm out horizontally. I.e. you point in the direction you're turning.
for stop, it's a mess. It can be the same as the nearside turn, or with the arm strait up, or in some parts of the US, the arm horizontal with the forearm vertically down and the palm facing back. I think of this as "holding those behind back".
In additional, many places allow point in the direction you're turning for turns in either direction.
I have not seen any updates to the cavalry-style stop sign.
What is a cyclist to do?
Any time you suspect there are riders behind, you need to take extra care, because you are the one who can see ahead, and they cannot.
So when approaching the kind of situation described in the linked question, if you can see the situation developing before you arrive, it's time to start signalling (with the palm vertically down and facing back) to those behind so that they can be ready to stop. In this case you're already using your brakes lightly with the other hand if you can.
If you don't get any warning, there's no time to be gentle. Call out loudly that you're braking / stopping, and get on the brakes asap. Try to feather the brakes if you have room, so that those behind have a better chance of avoiding you.
An advantage of calling out is that with a loud enough call even the motorist can hear you. (I swear I've moved whole cars sideways this way).
Why palm vertically down, facing backwards?
Cyclists who ride close together tend to be road cyclists, and because of the position they tend to ride in, they will more easily see a low signal than a high one. And to make the high cavalry-style signal, you need to sit up, which is the opposite of what's needed for braking. And we can get our hand back on the brakes more easily from the low position too.
So, is it a thing?
Well, yes. But not an officially or universally accepted thing.