League of Legends (LoL) Question: Crit

No. If you crit on such an attack, the base damage will crit but the additional damage won't.

As a general rule of thumb, crit only deals damage off of your base attack damage; that is to say, it does not boost itself off of abilities. The only way to increase crit damage is to build more attack damage items. There are exceptions to this rule, mainly Yasuo's Q. This is because his Q is treated as a basic attack, so it can crit off its own damage. There are a few other champs who have abilities that can crit. The ability will say so if it can. All basic attacks can crit off of their base damage.