Garlean in general might not able to conjure or weave Aether, they still can use Dynamis as the power source or use technology to weave Aether.

Jobs that use very little of Dynamis and Aether,
Reaper

Jobs that mainly use Dynamis as main source of power, and with some Aether usage.
Dark Knight
Warrior
Bard
Dancer

Jobs that have a balanced usage of both Dynamis and Aether
Dragoon
Samurai
Monk
Paladin
Astrologian
White Mage
Red Mage

Job that mainly use Aether as main source of power, and only use Dynamis in form of Limit Break
Gunbreaker
Black Mage
Summoner
Scholar
Sage
Machinist
Ninja

Garlean should able to became Warrior, Bard, and Dancer due it's a more Dynamis oriented Class

However, GNB, Sage and Machinist despite being an aether heavy job, these job are also more technology focused, thus it can circumvented with artificial tools such as Aether Cartridges

Lore wise, DRK don't really use Aether , only does gameplay wise as edge/flood of shadow cost MP to use. Therefore, a Garlean shouldn't have any no trouble becoming a DRK so long the said Garlean is not a psychopath.

Summoner too despite being an Aether heavy job as well, but Ultima Weapon has perfectly demonstrated how to harness Primal power without needing to summon one, as all Garlean need to do is condense the Ultima Weapon's Primal Summoning Technology into a codex.