The (very) short answer is: “No, monks don’t gempukku”.
To quote the source material for OP’s quote (Winter Court: Kyuden Asako):
The order of the Togashi monks, of course, has no gempukku ceremony. They instead require applicants to achieve a certain state of mind before accepting them fully into their ranks. This spiritual and emotional journey is represented physically by the individual’s arduous climb to reach Kyuden Togashi.
So they explicitly don’t have a gempukku but they do have a rite of passage.
That said, the Togashi have always been weird. While there are Togashi who are bushi, there has been at least one canon Togashi monk who wields the daisho, which is something only a samurai should be allowed to do. Such behaviors are tolerated in part because the Togashi family is a samurai family, nevermind that most of its members are former peasants become monks. The other reason is simple, stubborn tradition. That being the tradition of going:
“The Dragon are doing a thing.”
“Who cares. Dragon are weird.”
“Okay, but he’s a monk.”
“Oh, geez. Those are even weirder.”
“So what are we going to do about it.”
“Eh, as long as they stick their mountain, why bother to do anything.”
So I don’t see anything in the statement that it is RARE for the Tattoed Men to participate in gempukku that contradicts the broader statement of Kyuden Asako. However...
There are a LARGE number of deviations from the generally accepted Rokugani mythos in the Beginner Box module. For one thing, the gempukku in the intro module is treated as being the gempukku for everyone although traditionally it has only been the gempukku for the Crane. Likewise, the gempukku has traditionally been a measure of whether one is ready to become a samurai as determined by their sensei and school, with the consequence of failing being nothing more than further training. Still worse, the module has everyone competing in the iaijutsu tournament, including courtiers, shugenja, and yes... even monks.
I see 3 reasons why this would be the case:
- The narrative author did not have a firm understanding of prior canon.
- The narrative author was seeking to displace prior canon.
- The narrative author knowingly allowed some lapses in prior canon in order to make the intro game more accessible to new players, by making circumstances more similar to something one might experience in D&D while holding out the bits they felt were important for new players to grasp. This is not uncommon to see among the Heroes of Rokugan organized play intro modules, though much of that is up to how the GM runs it.
Which will probably not be answered until Emerald Empire’s is released. At which point it may be up to the community to decide what the “proper” canon is, as it has done with prior inconsistencies between editions.
But again, the short answer is: “No, monks don’t gempukku”.