They also wrote:
"However, when the value of Treasure Hunter placed on a monster and the value of the Treasure Hunter on your character are different, this will cause the growth rate to vary. With that said, if you want to increase the Treasure Hunter value, it is best to utilize equipment that has the Treasure Hunter+ effect. By unequipping Treasure Hunter+ gear, you are essentially creating a gap between the value placed on the monster and your character, which results in an inefficient means for increasing the TH value."
Maybe I'm missing something, but does this not pretty clearly mean that yes, the chance for triggering the value going up is affected by the difference between your treasure hunter level, and the one currently on the enemy?
It's also how it always felt to me in practice. For example, if the monster is currently at treasure hunter at level 4, and I go at it with 8, leveling it up will likely trigger much faster than it would when staying at 4.
Testing just how big of a difference there would be between 4 and 5 versus 4 and 8 would probably take a silly amount of time, and I'd definitely rather go for 8 in any case, but that's me. ^^
As for the critical question, I don't think that one has an effect on this, but I would not be surprised if it did...