I need to know so I don't have to do some intense RNG breeding
Yes it will be allowed as long as it doesn't have any suspicious attributes or invalid traits, your Pokemon will be able to battle in Wi-Fi battles It basically just needs to follow the requirements listed in the validness checker I used to explain a similar in a similar problem just with a Torterra then: Seeing as the Random Matchup uses the same validness checker as Pokecheck does, if your Pokemon is not too suspicious according to Pokecheck, it will be valid for the Random Matchup :)