This has happened before, it'll do a simple script check
//if the input fields are equal to database values, no need to update and waste resources,hence, do nothing:
if ( (shioban_mooney = 1) //where 1 is complete 0 is incomplete
{
//do nothing
}
//If, however, (they are NOT equal and) input fields are not empty:
elseif (shioban_mooney = 0)
{
//do something.
}
They even stated that 'quests cannot be completed when the event has ended', meaning if you don't finish it now, you'd have to wait until February to complete it.
The gear quest is a one time thing, technically you can wait and do the gear quest until then but it will NOT repeat it.
Square Enix won't repeat a quest that drops event gear.
As for the AF comment, that was me referring to having 'two sets of an item', not the gender locking scenario, where-in if you already had AF from 1.0, but it wasn't in your inventory/armory chest at the time, it would give you a second (un-discarable) item.
