So what I’m asking is that if a uncommanded nose pitch up happened and was so bad that it reached a pitch angle of 50 degrees, the pilots were unable to stop the pitch up by applying the control column forward, would it be justified if the pilots just applied more back pressure, ultimately doing a full loop?
No airliners aren't stressed for loop maneuvers. The proper action for that kind of extreme pitch attitude is to roll 90 degrees and let the nose fall, then roll level as the horizon is passing. Of course if you had a nose up stab trim runaway that left you stuck with that pitch tendency (effectively a much lower trim speed), you're back to square one.
You have to slow down to as close as you can get to the trim speed that the nose-up-stuck stab wants to fly at. You might find that you have enough elevator authority to maintain a level pitch attitude if you get the speed down to a minimum flaps up speed, say 180kt.
Then you can do other things to create a nose down pitching moment, like dropping the gear, and on most airplanes, extending flaps. That should be enough to remove most or even all of the elevator input required depending on where the stab was when you killed its runaway. In an extreme case where you've run out of options, you might even try getting passengers to move forward.
In recurrent sim training, a nose up stab runaway was always a more pleasant exercise than a nose down one. Mostly because slowing down, and gear and flaps helped, and to the extent you had to hold continuous nose down elevator, one of you could brace your knee against the column to help with most of the push force and it was easier to hold it for extended periods. A nose down stab runway was a much more difficult situation.
Well, in the world of radio-controlled model airplanes, there are some aircraft (e.g. long-winged gliders) that are prone to entering an uncommanded nose-down "tuck", which is best escaped by giving a firm nose-down input to fly through half of a downward loop to enter inverted flight.
But if I were a passenger in a plane that was doing an unexpected loop, I would probably be frowning.
Anyway, as far as normal (upward) loops go-- you really don't want to mess around with off-the-cuff spur-of-the-moment loops unless you know with absolute certainty that you are entering them with sufficient airspeed and pulling sufficient G's to get well past the upside-down attitude with sufficient flying speed. Otherwise you are in danger of entering of a tailslide after running out of airspeed with the nose pointing steeply upward. Very bad for the control surfaces.
Of course, retaining too much airspeed as you transition through level inverted flight into the start of an inverted dive, can also be a very bad thing.
So be careful when looping.
Basically, a loop is never going to be a practical approach to dealing with something that is unexpectedly going wrong with a conventional full-scale airplane, unless something is seriously broken in the control system, and maybe not even then. In almost all cases of an unexpected pitch-up, it would be better to increase the bank angle to help bring the nose down, if elevator inputs alone are somehow not doing the job.
No it would not be a good idea, nor justified and it would be frowned uppon, aside from the fact this is not a great idea for an untrained pilot this would simply stall the plane. Most aircraft lack the thrust to do a full loop in this manner. Pulling up aggressively even at full power generally leads to a "power on stall"