If the Pokemon is already level 100, it can't level anymore. While EVs can be earned freely, they are not applied until the next time the Pokemon levels up.
Also because the only way to reach level 100 without filling EVs is to use 99 Rare Candies or the daycare, because all battle EXP also gives EVs. The raw amount of EXP you need to level at high levels makes it highly unlikely you would have EVs left to gain.