So I've read through this thread for the pertinent info on the "Elevator Trim Up" issue, and I see where most everyone uses words like "tighter" as the advantage gained. However, I wonder if the more correct term, at least in the scenario I'll present here, is "quicker".
I'll just give you what I was taught and the reasoning behind it. I'll even admit that it 'seems' to actually induce some small element of advantage, at least to my perception, but I could be technically wrong, so don't beat on me, just explain.
When entering into a Head On merge with a bandit at some distance (similar to the dueling merge we use to practice ACM) I will sometimes hit the Elevator Trim Up key at about 2.5-3K out from the bandit. This drives my nose up so I counter with forward pressure on the stick. It takes approx. a second and a half for the elevator to move from neutral to full up. As I avoid the bandit's shot and we pass I release stick pressure and my plane seems to immediately snap up into a full elevator up loop. The bandit, I assume, pulls back on his stick to achieve the same loop, but it takes time for his elevator to get into the full up position. Therefore, all other things being equal (we react into the loop at the same time), theoretically, I gain a split half second advantage as my elevator is already full up at the moment in initiate movement upward out of level flight. Does this mean I actually turn tighter, I don't know (you'd think so), but I think it does mean I turn a slight bit quicker.
However, I'm open to the interpretation of the 'experts' that maybe even this is a fallacy.
Also, I fully realize that in doing this you induce drag at the merge, but given a high starting speed this is not a problem, further it seems to help to quickly reduce airspeed for a better loop as well.