Yes, if it's too "fat" to go through a 1/4" slot, it will be too fat to go through their automatic sorting machines. It has to be hand cancelled, which ends up costing more $$.
I've found that if I make all my candy packages at the start of the swap, and put the cards into envelopes then, the fabric will compress together to make it even flatter by the time I'm set to mail it. I buy cards big enough to have 6 stacks of 8 candies in them, without the stacks overlapping. Then I add the last two (to make 50) on top. I don't fool with plastic wrap. That's the flattest way I know to send them.