Yes, if you're doing organized play, random card rewards come from your class deck box instead of the game box. From the OP Guide:
"The procedure for earning scenario rewards (or adventure rewards, or adventure path rewards) follows the standard rules with one exception: If you are rewarded with a card from the box, you will instead take a random card of the same type from your Class Deck box. The card you take cannot have an adventure deck number higher than that of the scenario you completed."
Also, back to the Flenta issue, I had an interesting thought. If a Flenta player has at least one spell card feat and is playing with a box that has the add-on deck, she can cast all of her spells and exploit a loophole with Charm Animal. Normally, real spellcasters have to bury the card so they can only gain one animal ally each scenario. Flenta, on the other hand, has to banish it, but can get it right back due to her power. So she can try to go fishing during a scenario and get as many of the animal allies as she can (7 at Adventure 4). Since she can recharge instead of discard her weapons and essentially auto-recharges spells after a point, she can cycle her deck pretty efficiently if played right. This can be enhanced further with role powers. But of course, bad luck with location or plunder pulls can screw the whole thing up.