Thanks to @Kaphotics for pointing me in the right direction. I took the past few days to analyze the randomization mechanic for local events. I also figured out how offset 0x205 in WCFull is used.
As we know in Gen 7 you can only receive a wondercard that you have not received before in the set. It turns out that 0x205 can determine the likelihood of which one you get. Every WC in the distribution set gets a base weight of 1 (even if set to 0). The wondercard gets added to a list the same number of times equal to the weight. So if the weight is 5, it gets added 5 times. This is akin to filling a jar of M&M's and picking one out at random.
This has interesting ramifications (if it ever gets used). As we know, when offset 0x204 is equal to the number of WCs in the set (like eeveelutions), the player receives each WC uniquely once, and then subsequently receives one at random. This means that 0x205 determines how likely a person would be to get the "rare" WC again.
if offset 0x204 is higher than the number of WCs in the set (like the anime pokes), then the player can only receive a total number of WCs equal to the number of WCs and cannot receive any duplicates. For example, if there are 3 WCs in the set, but 0x204 is set to 4, then you can only receive each WC once and no duplicates.
if offset 0x204 is LOWER than the number of WCs in the set (we haven't seen this yet), then the player can only receive a total number of WCs equal to the counter.
The likelihood of a pokemon increases as you receive them because the probably of the pokemon (presumably common ones) that were already received are not included in the total weight. So if there are 5 pokemon, 1, 10, 10, 10, 10, then the first time the rare is 1/41, while the next time it is 1/31, etc.
And as an interesting note, it looks like the max number of wondercards in a distribution is 20 and the maximum weight is 255. That means the list can have up to 5,100 entries (20.4KB memory), and minimum odds of 1/5100, and a maximum of 1/1 (single pokemon). I personally think it is a terribly written mechanic compared to 5th anniv eggs during the GBA era.