Judging by that statement right there, I'd say no. The way the armoury system is built classes = weapon types. You switch classes by switching weapons. Not that it would be impossible but any secondary weapons a class gets access to would have to be exclusive to that class, not to mention the jobs by extension would have to have access to them as well. I can't see jobs getting any weapons their base classes don't either, considering you have to go Class > Job. Let me put it this way:
*If Gladiator can use Sword and Greatsword but Paladin can only use Sword, you ALWAYS have to carry a Sword with you if you want to use Paladin regardless of whether or not you use it on Gladiator.
*If Paladin can use Sword and Greatsword but Gladiator can only use Sword, you ALWAYS have to carry a Sword with you if you want to use Paladin since you must switch from the class first to the job.