Ranger would obviously get in the action, despite it not being mentioned very much. Ninja has A- throwing, the highest of the bunch, and gets access to expendable weapons nobody else does, so they'd probably get in.
Dancer is also one of the four jobs that are on Chakram like Ninja, but also gets the War Hoop, their artifact weapon, so they'd probably get in too. Blue Mage only gets access to swords and clubs, so assuming they'd finally get throwing skill natively, they'd be likely to be a job that can use throwing weapon skills, especially since they're on Chakram like Ninja and Dancer. Thief, which is on Boomerangs with Ranger, and Chakrams like Ninja, Dancer, and Blue Mage, is also a likely candidate for weapon skills.
The rest of the jobs are considerably less likely to get in with native throwing weapon skills, especially if there ends up being no weapon skills for expendable ammo. However, some are more likely then others, and I'd think we'd see two or three of these jobs getting in, particularly Warrior.
Warrior is the most likely outside the group of RNG/NIN/THF/DNC/BLU to get throwing skills just because they have access to so many weapon skills, but also because they're on select Boomerangs, and have Dart and Bomb access too. Corsair, which is specially ranged based like Ranger, and even has a pretty high throwing skill, might get considered, especially since they get so many Darts, however this may be iffy. Red Mages are on Darts and have a tiny bit of skill (the dismal F skill, below that of even Bards or White Mages), so they'd be in a even less likely position to get them, while still having a very small chance for expendables.
Black Mage and Scholar both have D rank skill in throwing, which is about what Warrior gets, but both are very backline magic casters that don't traditionally get weapon skill access on any weapon they're given, even on Staffs. Still, they get access to actual throwing weapons - Pebbles, Tathlums, and Astragolos, unlike a job like Samurai, so there is very slightly more hope for them to have native skill then Samurai. Scholar would be slightly less likely then Black Mage since they carry more book-type ammo in their throwing slot (although books as a throwing weapon isn't unheard of in FFXI!). Bards have slightly lower skill and the same weapon access, but are unlikely since they're constantly carrying instruments.
Monks also have lower skills and the same access, but are more likely then Bards, and probably way more likely then Black Mages and Scholar since it is a combat class, and Monks tend to be fairly good with all their blunt weapons, but like them, have pretty bad odds of actually getting a weapon skill (probably second or third place after Warrior though, depending on the other Blunt heavy job). White Mage has poor skill, like Monk, and the same access, but also like Monk, White Mage traditionally has very limited weapon selection that they get roughly every weapon skill the weapon has that isn't tied to a weapon or Nyzul Isle.
Samurai are unlikely to be considered despite their high skill for native skill, because they're just not on anything unless Throwing Coins are ever implemented into the game. Puppet Master is even less likely, since they didn't even get any hints at weapons, and they're constantly holding their Animators. Other jobs without skill probably won't be considered, despite Dark Knight having Dart and Bomb access, or Summoner having Astragolos and Pebbles.
The hierarchy for current likelihood to get put on throwing weapon skills is probably roughly something like this: RNG >> NIN > DNC > THF > BLU >>>> WAR >> MNK=WHM > COR >> RDM >> BLM/SCH > BRD >> SAM > PUP > DRK >> SMN > BST > DRG >> PLD